I learnt about ZKP recently from a friend. Thanks for writing this, it was an interesting read.
Reading this makes me think ZKPs are somehow related to Property testing, isn't it? Because in property testing the goal is to probabilistically check proofs. Here in this article for example, the property of the answer is that it should have numbers 1 to 9 in every row, column, and box.
Another property is that there is only one solution.