Existing probabilistic privacy enforcement approaches permit the execution of a program that processes sensitive data only if the information it leaks is within the bounds specified by a given policy. Thus, to extract any information, users must manually design a program that satisfies the policy. In this work, we present a novel synthesis approach that automatically transforms a program into one that complies with a given policy. Our approach consists of two ingredients. First, we phrase the problem of determining the amount of leaked information as Bayesian inference, which enables us to leverage existing probabilistic programming engines. Second, we present two synthesis procedures that add uncertainty to the program’s outputs as a way of reducing the amount of leaked information: an optimal one based on SMT solving and a greedy one with quadratic running time. We implemented and evaluated our approach on 10 representative programs from multiple application domains. We show that our system can successfully synthesize a permissive enforcement mechanism for all examples.