Bayesian updating of atomic probabilities

The standard conditional probability formula is supposed to reflect the correct updating of probability assignments when new information is incorporated (Bayesian updating). We consider a context with no preferences on outcomes. Starting from an atomic probability measure and assuming a “minimum requirement” relational assumption or other stronger assumptions, we characterize the family of probability measures where Bayesian updating is the only possibility. This family turns out to be formed by those probability measures in which the Laplace formula can be used to determine the probability of events.