In many applications of zero knowledge proofs, you prove knowledge of solution to a puzzle that need not have a solution. E.g. graph isomorphism, a 3-coloring,

In many applications of zero knowledge proofs, you prove knowledge of solution to a puzzle that need not have a solution. E.g. graph isomorphism, a 3-coloring, a Sudoko puzzle. So the probability of guessing the solution can be 0, while there's a nonzero probability of convincing a verifier.