This study proposed a probabilistic methodology based on a confidence interval with the aim of overcoming the limitations of deterministic methods. A stability evaluation technique was required because the output variability of renewable energy can lead to instability of the distribution system. The proposed method can predict the possibility of violating stability in the future. It can also provide a theoretical basis for securing distribution system stability and improving operational efficiency by assessing the in-stability risk and worst-case scenarios. Because of steady-state analysis in the distribution system to which solar power is connected, the probability of violating the standard voltage during the daytime when PV fluctuations are severe was the highest. Moreover, as a result of a simulation of a three-phase short-circuit in the distribution system that is connected to the PV and WT, it was observed that it could violate the allowable capacity of the CB owing to the effects of the power demand pattern and output variability.