Business processes from many domains like manufacturing, healthcare, or business administration suffer from different amounts of uncertainty concerning the execution of individual activities and their order of occurrence. As long as a process is not entirely serial, i.e., there are no forks or decisions to be made along the process execution, we are - in the absence of exhaustive domain knowledge - confronted with the question whether and in what order activities should be executed or left out for a given case and a desired outcome. As the occurrence or non-occurrence of events has substantial implications regarding process key performance indicators like throughput times or scrap rate, there is ample need for assessing and modeling that process-inherent uncertainty. We propose a novel way of handling the uncertainty by leveraging the probabilistic mechanisms of Bayesian Networks to model processes from the structural and temporal information given in event log data and offer a comprehensive evaluation of uncertainty by modelling cases in their entirety. In a thorough analysis of well-established benchmark datasets, we show that our Process-aware Bayesian Network is capable of answering process queries concerned with any unknown process sequence regarding activities and/or attributes enhancing the explainability of processes. Our method can infer execution probabilities of activities at different stages and can query probabilities of certain process outcomes. The key benefit of the Process-aware Query System over existing approaches is the ability to deliver probabilistic, case-diagnostic information about the execution of activities via Bayesian inference.