In this paper we consider the on-line max query auditing problem: given a private association between fields in a data set, a sequence of max queries that have already been posed about the data, their corresponding answers and a new query, deny the answer if a private information is inferred or give the true answer otherwise. We give a probabilistic definition of privacy and demonstrate that max queries can be audited in a simulatable paradigm by means of a Bayesian network. Moreover, we show how our auditing approach is able to manage user prior-knowledge.