I found the Sudoku example more illustrative, where you want to share your knowledge of the solution without sharing the solution itself. In that case, others do indeed care about the details of your knowledge.
You can't just provide a hash of the solved board and say "lol solved it", as only those who had also already solved it could verify your statement. Maybe I don't trust those others who claim they also solved it, how can I verify that indeed you solved it? You could tell me the solution but then you'd ruin the puzzle for me, which is no good.
So as I understand it, the point of ZKP is that they allow you to share proof of your Sudoku solution to me, in a way where I can be certain you do indeed have the right solution, without me learning what exactly the solution is.
