A Business Process (BP) consists of some business activities undertaken by one or more organizations in pursuit of some business goal. Tools for querying and analyzing BP specifications are extremely valuable for companies. In particular, given a BP specification, identifying the top-k flows that are most likely to occur in practice, out of those satisfying a given query criteria, is crucial for various applications such as personalized advertizement and BP web-site design. This paper studies, for the first time, top-k query evaluation for queries with projection in this context. We analyze the complexity of the problem for different classes of distribution functions for the flows likelihood, and provide efficient (PTIME) algorithms whenever possible. Furthermore, we show an interesting application of our algorithms to the analysis of BP execution traces (logs), for recovering missing information about the run-time process behavior, that has not been recorded in the logs.