Are zero knowledge proofs probabilistic?

Question

Does the interaction between prover and certifier yield a 100% certain proof? If I understood correctly this procedure is based on iterative checks by the certifier which keeps trying until it's satisfied with the reliability of the certificates. So it can be satisfied to arbitrarily high degree but not fully satisfied. Did I get it right?

Answer 1

Yes, they are probabilistic in nature.

As quoted from wikipedia:

Zero-knowledge proofs are not proofs in the mathematical sense of the term because there is some small probability, the soundness error, that a cheating prover will be able to convince the verifier of a false statement. In other words, zero-knowledge proofs are probabilistic "proofs" rather than deterministic proofs. However, there are techniques to decrease the soundness error to negligibly small values.

With more iterations, the probability of cheating decreases but it is not really a proof. It is not $100\%$.