Over the past decades, the deployment of distributed generations (DGs) in distribution systems has grown dramatically due to the concerns of environment and carbon emission. However, a large number of DGs have introduced more uncertainties and challenges into the operation of distribution networks. Due to the stochastic nature of renewable energy resources, probabilistic tools are needed to assist systems operators in analyzing operating states of systems. To address this issue, we develop a probabilistic framework for the assessment of systems. In the proposed framework, the uncertainties of DGs outputs are modeled using short term forecast values and errors. Moreover, an adaptive cluster-based cumulant method is developed for probabilistic load flow calculation. The performance of the proposed framework is evaluated in the IEEE 33-bus system and PG&E 69-bus system. The results indicate that the proposed framework could yield accurate results with a reasonable computational burden. The excellent performance of the proposed framework in estimating technological violations can help system operators underlying the potential risks of systems.