In those days was Hezekiah sick unto death. And the prophet Isaiah the son of Amoz came to him, and said unto him, Thus saith the LORD, Set thine house in order; for thou shalt die, and not live. Then he turned his face to the wall, and prayed unto the LORD, saying, I beseech thee, O LORD, remember now how I have walked before thee in truth and with a perfect heart, and have done that which is good in thy sight. And Hezekiah wept sore. And it came to pass, afore Isaiah was gone out into the middle court, that the word of the LORD came to him, saying, Turn again, and tell Hezekiah the captain of my people, Thus saith the LORD, the God of David thy father, I have heard thy prayer, I have seen thy tears: behold, I will heal thee: on the third day thou shalt go up unto the house of the LORD.
Hezekiah is told flatly to set his house in order because he will not live, turns his face to the wall and weeps, and is granted fifteen more years. It is one king at one moment, told as a story about him, not as a rule about how illness goes.