In 1 Samuel 20:31, Saul tells Jonathan that David was a direct, major threat to his reign:
For as long as the son of Jesse lives on the earth, neither you nor your kingdom will be established. Therefore now, send and bring him to me, for he must surely die.
In 1 Samuel 23:17, Jonathan states that both he and Saul were aware that David would become king:
Thus he said to him, “Do not be afraid, because the hand of Saul my father will not find you, and you will be king over Israel and I will be next to you; and Saul my father knows that also.”
In 1 Samuel 24:20, Saul states that he knew that David would become King:
Now, behold, I know that you will surely be king, and that the kingdom of Israel will be established in your hand.
My question is how Saul found out about this. From 1 Samuel 16:1-3 (NASB):
Now the Lord said to Samuel, “How long will you grieve over Saul, since I have rejected him from being king over Israel? Fill your horn with oil and go; I will send you to Jesse the Bethlehemite, for I have selected a king for Myself among his sons.” 2 But Samuel said, “How can I go? When Saul hears of it, he will kill me.” And the Lord said, “Take a heifer with you and say, ‘I have come to sacrifice to the Lord.’ 3 You shall invite Jesse to the sacrifice, and I will show you what you shall do; and you shall anoint for Me the one whom I designate to you.”
This implies that Samuel was at least somewhat secretive about his intention to anoint David King. That being the case, how did Saul and Jonathan find out about this? How widely known was it that David had been anointed King?
Also, the text strongly implies that Saul may well have killed Samuel if he found out (see the linked question as well). Why didn't he ever retaliate against Samuel in any other way if he knew (especially given that he evidently had no qualms about killing priests for petty reasons)? (I can move this last point to a separate question if people think that it should be its own question).