The generalized stabilization problem of singular Markovian jump systems(SMJSs) with stochastic nonlinear perturbation is discussed, where the existence of nonlinear perturbation belongs to some probability. By exploiting the Bernoulli variable to describe whether the nonlinear perturbation exists or not, a kind of model for such systems is firstly established. Based on the obtained criteria, new sufficient conditions for the existence of both mode-dependent and mode-independent controllers are given as strict linear matrix inequalities(LMIs). Different from the existing results, several general conditions on stochastic admissibility depending on such a probability are developed, where the uniqueness and sufficiency of solution is also guaranteed. Because of such a probability considered, the corresponding results are less conservative. Finally, numerical examples illustrate the utility and superiority of the presented results.