Multiple-contingency and wind power integration add difficulty for probabilistic short-circuit analysis (PSCA). The power flow model with doubly-fed induction generators (DFIGs) is introduced, which together with wind uncertainty yields initial state before contingency. The multiple-contingency algorithm is introduced to find expectation, variance, and distribution of the bus voltages and the branch currents. A hybrid probabilistic sampling technique is proposed with the fault branch enumerated and probabilistically weighted, and other fault parameters sampled. The variance for the hybrid simulation is proposed by combined analytical enumeration and probabilistic sampling. Numerical analysis quantifies impact of wind fluctuation and double contingencies on the PSCA results, and compares convergence of sequential voltages and currents. The proposed models provide reference to select electrical equipment and analyze power system security.