We propose a fully probabilistic extension of Event-B where all the non-deterministic choices are replaced with probabilities. We present the syntax and the semantics of this extension and introduce novel and adapted proof obligations for proving the correctness of probabilistic Event-B models. As a preliminary step towards handling refinement of probabilistic Event-B models, we propose sufficient conditions for the almost-certain convergence of a set of events and express them in terms of proof obligations. We illustrate our work by presenting a case study specified in both standard and probabilistic Event-B.