When dealing with real-world processes, it is essential to consider their inherent uncertainty to more accurately represent their nature. In this work, we consider cases in which some information in the log might be unreliable. We propose a novel semantics for probabilistic process traces, based on the Distribution Semantics from Probabilistic Logic Programming, which allows one to annotate event executions of an observed trace with a probability representing the uncertainty of the event as the degree of our belief in that event happening. Then, we propose a novel definition of probabilistic compliance of a probabilistic process trace w.r.t. a declarative process specification, and how to compute it using a probabilistic abduction proof-procedure. Experimental results on a real-world healthcare protocol are presented to evaluate the feasibility of the proposed semantics on conformance checking.