John Chrysostom
Why does Christ ask this? In order to expose the Jews' evil intent.
Pilate had already heard about this from many. But because the Jews could say nothing, he decides, to avoid a lengthy investigation, to bring forward the very charge they had always made against Him.
Besides, when he said to them, "Judge Him according to your law," they wished to show that His crime was not a Jewish matter.
They answered, "It is not lawful for us," meaning that He is not guilty against our law, but that His guilt is political.
Pilate understood this. Therefore, as if danger threatened him personally, he says, "Are You the King of the Jews?"
Consequently Christ asks him not out of ignorance, but says, "Did others tell you?" so that Pilate too might accuse the Jews.