Process mining is a means to extract hidden information from the event logs accumulated by the information systems that drive increasingly complex business processes, potentially improving their manageability. Traditional process mining is used mainly to extract a useful description of how an enterprise’s processes actually work (as versus how they are documented to work), usually presented in the form of a flowchart. To the best of our best knowledge, previous process mining techniques have not used available information on duration and frequency of portions of a business process. We propose a method that combines process mining with Bayes’ Theorem to augment a mined model with probabilities information. This additional information increases the value of the mined model and can be used not only in making predictions, but also in making decisions. Together with activity-based costing that assigns some cost to each activity in a process, our process mining technique can measure the expected costs of different stages in the process to support improvement of the underlying processes. We apply our approach to a chip probing process of a semiconductor firm in Taiwan. Our results confirm that the proposed approach could improve company decisions regarding their internal supply chain management.