Reo is a channel-based coordination language that allows the construction of connectors to coordinate behavior among different components in distributed systems. Probabilistic connectors in Reo capture the random and probabilistic behavior to deal with the uncertainty of the real world. In this paper we use PVS to provide a mechanical formalization for probabilistic connectors. We first present the formalization of random/probabilistic channels and the composition operators in PVS. Random and probabilistic channels are modeled as relations on timed data distribution sequences that are observed at the source and sink ends of these channels. Composition operators are used to combine random/probabilistic channels together with primitive channels to construct complex component connectors. The approach can be used to naturally specify complex connectors and prove important properties for probabilistic connectors as well as the refinement/equivalence relations between them with the PVS proof assistant.