Event-B is a state-based formalism that enables the correct-by-construction development of systems. Several works have focused on the extension of Event-B for the description of probabilistic systems. While these extensions of Event-B allow replacing some non-deterministic choices with probabilities, some sources of non-determinism are left untouched. In this paper, we propose a fully probabilistic extension of Event-B where all the non-deterministic choices are replaced with probabilistic ones. We present the syntax and the semantics of this extension and illustrate our approach on a classical case study.