This paper addresses an issue in the contingency screening that the probabilities of some high-order N- k contingencies involving multiple element failures may be significantly underestimated in the traditional screening processes. Considering the severe consequences of these hidden contingencies, this practice would impose a potential risk to the system operations. In this paper, we propose a multi-stage approach to screen out these N- k contingencies and reveal their hidden probabilities. The approach is formulated as a bi-level mixed integer linear programming problem and validated by simulations on the IEEE 14-bus and 118-bus systems.