(Is this one of those questions which could actually be asked without biblical references, but still include some to avoid the close votes? I love those questions!)
First of all, Hebrew does have a definite article: prefixed ה. This is no less an article than English "the", French "le/la/les", etc., just because it is a prefix. Just like having pronominal suffixes (־וֹ for the 3rd person masculine singular) does not mean that Hebrew "doesn't have" personal pronouns in direct object environments. (But this is just being pedantic.)
What does complicate the matter in Hebrew is that the definite article is not always visible in the consonantal text. There are several phonological rules related to the definite article. Most importantly perhaps, when the definite article follows one of the prepositions בְּ/כְּ/לְ, it disappears and the preposition gets a patach/qamets vowel. With this vowel it can be recognized that the noun is definite. This is for instance the case in Gen. 1:5, where we have לָאוֹר, with a qamets, as opposed to e.g. Isaiah 5:20, where we find לְאוֹר, with a schwa (the meaning there fits indefiniteness: "woe to those ... who put darkness for light").
The synchronic rules as will be taught by most textbooks can roughly be describes as follows (though the author also notes that in real the rules would be more complicated):
If one were to write a synchronic rule-grammar for Hebrew, the definite article could quite legitimately be given a base form *han-, from which appropriate phonetic rules would lead to the actually attested forms. These rules would include (1) the assimilation of n to a following consonant; (2) the gradual loss of gemination with certain guttural consonants, accompanied by the compensatory lengthening of a to ā; (3) the dissimilation of a to e in certain environments; and (4) the syncope of h after the prepositions bə, lə, and kə.
Lambdin, 1971. 'The Junctural Origin of the West Semitic Definite Article', in Goedicke (ed.), Near Eastern Studies in Honor of William Foxwell Albright, pp. 315–333.
To take Gen. 1:5 again as an example: we there have לָאוֹר lā'ôr. The synchronic analysis would be that לְהַן אוֹר lə-han 'ôr through (1) becomes לְהַאּוֹר lə-ha''ôr (note the dagesh in the aleph), but since aleph cannot be geminated (=have a dagesh) (2) we get לְהָאוֹר lə-hā'ôr and by (4) we get לָאוֹר lā'ôr. This is opposed to the form without definite article, לְאוֹר lə'ôr which does not follow any of those sound changes.
The choice for han is of course not arbitrary. The n assimilates in many environments to the following consonant (i.e. rule (1)). This can also be seen in the preposition מִן which often appears without nun (and the next consonant geminated). This also happens in verbal roots starting with nun.
Definiteness is a complicated category. It is very difficult to define what it means when a noun is definite, without using circular definitions. This discussion is not specific to Hebrew, and a good overview can be found in Lyons' 1999 Definiteness. Globally we can establish two methods:
- Familiarity: nouns are marked definite to mark to the reader/hearer that the referred entity is already known (familiar) to them. ("I saw a man and a woman. The man sat on a bench while the woman was walking down the street.")
- Uniqueness: nouns are marked definite when they are the only entity in context that can be referred to by the speaker/writer by that noun. ("Could you pass me the hammer?" - the hearer is not 'familiar' with the hammer but can resolve the reference)
Both methods have issues, and I would have given you an overview of Lyons' own position if somebody had not requested the book from the library while I had it checked out.
In any case, you must be prepared that the definite article does not appear in exactly the same situations as in English or other Western European languages, because it marks a slightly different semantic category. A well-known example is the "O king" in direct speech, as in 2 Kings 6:12 and numerous other places אֲדֹנִי הַמֶּלֶךְ, "my lord the king" literally.
As you may know, the definite article is omitted in genitive constructions ("the book of the king" is ספר המלך). Also, when a noun has a pronominal suffix (בנו "his son") it does not require a definite article, because the pronominal suffix already makes it definite. To say "a son of his" Classical Hebrew would use בן מבניו "(a) son from his sons"; (later Hebrew might use the numeral noun for "one" here, which has developed into an indefinite article later on.)
A good overview on the different semantic fields of the article is given by Barr, 1989, '"Determination" and the definite article in Biblical Hebrew', Journal of Semitic Studies 34(2), pp. 307–335.
Hebrew poetry is linguistically often very conservative. The definite article is much less frequent in the poetic texts. If you read French, a good starting point is Lambert, 1898, 'L'article dans la poésie Hébraique', Revue des Études Juives 37, pp. 203–209. While some say that the article is often left out in the B-part of verses (because it is implicit from the A-part), to my knowledge nobody really has a clue when the article is present and when it is not. For the book of Job, Sarna has put together a set of occurrences which seem highly inconsistent: Sarna, 1996, 'Notes on the Use of the Definite Article in the Poetry of Job', in Fox, Hurowitz, Hurvitz, Klein, Schwartz and Schupak (eds.), Texts, Temples and Traditions: A Tribute to Menahem Haran, pp. 279–284.
This lack of the article leads some scholars to translate many nouns as proper names, such as Michel in his 1987 Job in the Light of Northwest Semitic, vol. 1, for instance in Job 5:22, לְשֹׁד וּלְכָפָן תִּשְׂחָק, reading "At Violence and Starvation you shall laugh". However, this seems mostly triggered by translation possibilities, and it cannot be done consequently: for instance, in 5:26, we can hardly translate "grave" as a proper name, "you will come in full vigor to Grave" — and indeed here Michel adds "the".
Analysing the article in poetry is tedious, because of the textual history. When the article is only reflected in vocalization, it is quite possible that the noun was originally indefinite, and that the vocalization got corrupted by a scribe working at a time where the archaic origins of poetry were much less understood. Thus, to analyse the article in poetry it is best to focus on the "consonantal attestations", those where the ה is visible.
The origin of the definite article in Semitic languages is a bit troublesome as well. In Proto-West Semitic there was no definite article yet, but several descendants developed the article independently (see this Linguistics.SE post for background). Thus we have Arabic al-, Hebrew ha-, but also suffixes (Amharic -u and South Arabian -n).
According to Lambdin (1971; see above), the articles in Hebrew, Aramaic and Arabic have developed in similar ways. This is quite striking, because they are very different: Hebrew has ha-; Arabic al- but Aramaic has a suffix -ā (on masculine singular forms)! This is perhaps not the place to discuss the theory in depth, but in short the idea is that the article emerges from reanalysis of frequent word combinations, where the end of the first word becomes associated with the second word (or the start of the second with the first). This can indeed explain the emergence of definite suffixes and prefixes from an initially shared environment.