Hezekiah's praise for deliverance comes from God's saving him from death. He was suffering some sort of deadly infection from a boil. He was told his death was imminent. He wept before the LORD, praying for deliverance from death. God was gracious to the king and answered his prayer. Isaiah came to the king with good news. The king would live fifteen more years. God would save him.
And The Lord provided a miraculous sign to him, even as servants took Isaiah's medicinal advice and applied a folk remedy to the boil. The shadow of the sun retreated back down the staircase. The sun did not just stand still. It moved in reverse. The world changed direction briefly for Hezekiah and God to have a moment of grace. God will turn back time to show us His love.
The effect on Hezekiah was a song of praise. His thanksgiving is recorded for us. And we can sing it with him today because God is still the same. God still delivers us from destruction. He still teaches us the value of our sufferings as we trust in Him. He still delights in forgiving His children, casting all our sins behind His back.
I wonder if Hezekiah ever approached any staircase the same way ever again. Any shadow had to remind Him of God's powerful love and mercy. Perhaps every staircase in Jerusalem became a symbol of new life to him. After all, the God who turned back the shadow on the stairs had turned back death as well.