According to the gospel account by John, Jesus was asking for clarification from Pilate through a rhetorical question. That is, Jesus was clarifying with Pilate as to whether or not the indictment was second-hand (i.e., is it that others say that I am a King of the Jews?) versus Pilate himself. In other words, was the indictment because Rome saw Jesus as a king, or because others said that Jesus was a king? To put it another way, if there was no threat to Rome (since it was not Pilate accusing Jesus of being a king), then why is Jesus being charged at the instigation of third-parties?
When Pilate clarified that it was the former case (others accusing you of being a king), Jesus then indicated that this "kingdom" for which he was king had no fighters, and therefore was non-violent. (Thus there was no threat to Roman hegemony.) Jesus indicated that the essence of this kingdom was truth. Pilate rejoindered with "What is truth?" (John 18:38), and determined in the same verse that there was therefore no legal basis for an indictment to crucifixion (John 18:38).
So the reason that Jesus clarified with the rhetorical question to Pilate was to indicate to him (Pilate) that the charges against Jesus were a sham. The Apostle Paul indicates that the form (peacefulness) and substance (truth) of this testimony before Pilate provide the model to make ones confession before the world (1 Tim 6:13) -- that is, the follower of Jesus must present his personal Christian testimony with gentleness and reverence (1 Pet 3:15).
When Pilate had Jesus crucified, he placed the indictment for execution on the cross above the head of Jesus in three languages: JESUS THE NAZARENE, KING OF THE JEWS. In other words, Pilate was forced to crucify him as an instigator and threat to Rome, since the accusers of Jesus saw Jesus as a threat to Rome: "We have no king but Caesar." When these same accusers tried to get the wording for the indictment to crucifixion changed, Pilate saw this as an attempt by the accusers to show that he was crucified as a pretender king (John 19:21-22). Pilate denied the request, because to acknowledge that he was crucified for pretending to be a king would have negated the justice meted by Rome, since he was crucified as the bona-fide King of the Jews -- and thus Rome treated him appropriately as a threat to Rome. Otherwise there would have been no basis to crucify him. How would Rome have justified crucifying a self-proclaimed "king," whose so-called "kingdom" had preached peace (non-violence) and "truth" to its followers? Thus Rome crucified Jesus as "King of the Jews" because his accusers saw Jesus as a threat to Roman hegemony. Thus Pilate had responded with the sentence of crucifixion (per the statement placed above the head of Jesus on the cross, which was the legal indictment for crucifixion).