This paper studies top-k query evaluation for an important class of probabilistic semi-structured data: nested DAGs (Directed Acyclic Graphs) that describe possible execution flows of Business Processes (BPs for short). We consider queries with projection, that select portions (sub-flows) of the execution flows that interest the user and are most likely to occur at run-time. Retrieving common sub-flows is crucial for various applications such as targeted advertisement and BP optimization. Sub-flows are ranked here by the sum of likelihood of EX-flows in which they appear, in contrast to the max-of-likelihood semantics studied in previous work; we show that while sum semantics is more natural, it makes query evaluation much more challenging. We study the problem for BPs and queries of varying classes and present efficient query evaluation algorithms whenever possible.