Probabilistic conformance checking methods, which use the probability of observed traces to evaluate the fitness between process models and event logs, have recently attracted much attention. In this paper, we propose a new process model representation, the Probabilistic Generative Process Model (PGPM), which can explicitly calculate the generation probabilities of traces in a process model. PGPM can explicitly and quickly compute the trace probabilities in a process model by expressing the generation procedure of traces on the basis of a probabilistic context-free grammar. PGPM enables us to apply probabilistic conformance checking to various process models. We also propose a probabilistic parameter estimation method based on the expectation-maximization (EM) algorithm to obtain a superior probabilistic process model that locally maximizes the likelihood for an event log.