This paper investigates how set-containment queries over uncertain set-valued data can be efficiently processed. Based on the popular possible world semantics, we first present a practical model in which the uncertainty in set-valued data is represented by existential probabilities, and propose the probabilistic set containment semantics and its generalization - the expected Jaccard containment. Second, to avoid expensive computations in enumerating all possible worlds, we develop efficient schemes for computing these two probabilistic semantics. Third, we introduce two important queries, namely probability threshold containment query (PTCQ) and probability threshold containment join (PTCJ), and propose novel techniques to process them efficiently. Finally, we conduct extensive experiments to study the efficiency of the proposed methods. The experimental results indicate that the proposed methods are efficient in processing the uncertain set containment queries.