In complex event processing (CEP), simple derived event tuples are combined in pattern matching procedures to derive complex events (CEs) of interest. Big Data applications analyze event streams online and extract CEs to support decision making procedures. At massive scale, such applications operate over distributed networks of sites where efficient CEP requires reducing communication as much as possible. Besides, events often encompass various types of uncertainty. Therefore, massively distributed Big event Data applications in a world of uncertain events call for communication-efficient, uncertainty-aware CEP solutions, which is the focus of this work. As a proof-of-concept for the applicability of our techniques, we show how we bridge the gap between two recent CEP prototypes which use the same CEP engine and each extend it towards only one of the dimensions of distribution and uncertainty.