A sub-field of process mining, conformance checking, quantifies how well the process behavior of a model represents the observed behavior recorded in a log. A stochastic-aware perspective that accounts for the probability of behavior in both model and log is necessary to support conformance checking. However, existing stochastic conformance checking measures are not comparable for a broad framework that includes log-to-log (L2L), log-to-model (L2M), and model-to-model (M2M) comparison settings. Therefore, we propose a stochastic conformance checking measure based on the Jensen-Shannon Distance (JSD), which interprets models and logs as probability distributions over traces. It can be applied to perform L2L, L2M, and M2M conformance, while the latter requires approximation. Notably, it is the only known stochastic conformance measure that is a metric. JSD has been implemented and is publicly available. Our quantitative evaluations show the feasibility of computing JSD over real-life event logs, and that it provides diagnostic results different from those of existing measures. Moreover, experiments in the M2M setting confirm that our measure can be approximated using unbiased sampling.