If anything, the jester solidifies the king’s power by working for the king as a sort of pressure valve. The king wants some of the discontent of the people to be expressed openly, releasing built-up tension and ensuring that said discontent will not burst in actions that could really undermine his position. The jester is his means of doing that.
When we, the public, laugh at the king, our laughter is also an expression of his power. He wants us to laugh so as not to act. It is, then, his laughter grafted onto our faces. When we laugh at the king, it is actually the king laughing at us.
The king is still a human being. Refer to historical France and Russia for ways to deal with leaders who don’t listen to the people.