Plug-in electric vehicles (PEVs) have several capabilities to help the power system; for instance, one of them is participation in the energy market via vehicle to grid (V2G) technology. Due to some uncertain parameters such as battery state of charge (SOC), PEV availability, etc, they have stochastic behavior and it can affect the settlement of energy market. Accordingly, this paper proposes a framework for the stochastic clearing of electricity energy market in the presence of the PEVs while the uncertainties of PEVs and the synchronous generators are considered. The proposed stochastic energy market is cleared in two steps: at the first step, the random scenarios are generated using Monte-Carlo Simulation (MCS); then, at the second step, the stochastic market-clearing procedure is implemented as a series of deterministic optimization problems (scenarios) including non-contingent scenario and different post-contingency states. The network Total Cost (TC) is defined as an objective function and it is minimized for each scenario. In other words, the stochastic energy market is cleared based on the selection of the cheaper and proper energy providers, PEVs and synchronous generators, while the constraints are satisfied. The proposed optimization formulation is in the form of mixed integer nonlinear programming. Consequently, a heuristic based particle swarm optimization method has been adopted for the solution strategy. The effectiveness of the proposed method is examined based on a real case low voltage distribution system with 134 nodes.