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When operating in volatile environments, service-based systems (SBSs) that are built through dynamic composition of component services must be monitored in order to guarantee the response times of the SBSs. In particular, the critical path of a composite SBS, i.e., the execution path in the service composition with the maximum execution time, should be prioritised in cost-effective monitoring as it determines the response time of the SBS. In volatile operating environments, the critical path of a SBS is probabilistic. As such, it is important to estimate the criticalities of the execution paths and the component services, i.e., the probabilities that they are critical, to decide which parts of the system to monitor. In this paper, we propose a novel approach to the identification of Probabilistic Critical Path for Service-based Systems (PCP-SBS). PCP-SBS takes into account the probabilistic nature of the critical path and calculates path criticalities in the context of service composition. We evaluate PCP-SBS experimentally using SBSs that are synthetically composed based on a real-world Web service dataset.