Probabilistic skyline queries as an aspect of queries on uncertain data have become an important issue. Previous work on uncertainty modeling for probabilistic skyline queries only lies within the data. However, attribute values of uncertain data are influenced by contexts in real applications while uncertainty is also along with contexts. Further, previous work on probabilistic skyline queries only retrieves those points whose skyline probabilities are higher than a given probabilistic threshold. In this paper, we develop a novel probabilistic skyline query on uncertain data over uncertain contexts called UC-PSkyline, where possible world semantics model is utilized to model uncertain contexts. To avoid unnecessary pair-wise dominance tests, we devise an in-memory tree structure ZB*-tree to process UC-PSkyline queries efficiently. We also develop preprocessing and pruning techniques that can efficiently improve performance of UC-PSkyline. Experiments show the effectiveness and efficiency of the proposed techniques on real and synthetic data sets.