In semi-structured case-oriented business processes, the sequence of process steps is determined by case workers based on available document content associated with a case. Transitions between process execution steps are therefore case specific and depend on independent judgment of case workers. In this paper, we propose an instance-specific probabilistic process model (PPM) whose transition probabilities are customized to the semi-structured business process instance it represents. An instance-specific PPM serves as a powerful representation to predict the likelihood of different outcomes. We also show that certain instance-specific PPMs can be transformed into a Markov chain under some non-restrictive assumptions. For instance-specific PPMs that contain parallel execution of tasks, we provide an algorithm to map them to an extended space Markov chain. This way existing Markov techniques can be leveraged to make predictions about the likelihood of executing future tasks. Predictions provided by our technique could generate early alerts for case workers about the likelihood of important or undesired outcomes in an executing case instance. We have implemented and validated our approach on a simulated automobile insurance claims handling semi-structured business process. Results indicate that an instance-specific PPM provides more accurate predictions than other methods such as conditional probability. We also show that as more document data become available, the prediction accuracy of an instance-specific PPM increases.