Hezekiah said to Isaiah, “What shall be the sign that YHWH will heal me, and that I shall go up to the house of YHWH on the third day?”
2 Kings 20:8

Isaiah first told him he was going to die and then that he would recover. Asking for a clear sign to confirm a prophecy that seems to contradict a previous prophecy seems a reasonable request.

There also seems to be a veiled messianic prophecy in the king's question.