The critical path of a composite Web application operating in volatile environments, 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 Web application. In volatile operating environments, the critical path of a Web application is probabilistic. As such, it is important to estimate the criticalities of the execution paths, i.e., the probabilities that they are critical, to decide which parts of the system to monitor. We propose a novel approach to the identification of Probabilistic Critical Path for Service-based Web Applications (PCP-SWA), which calculates the criticalities of different execution paths in the context of service composition. We evaluate PCP-SWA experimentally using an example Web application. Compared to random monitoring, PCP-SWA based monitoring is 55.67% more cost-effective on average.