Higher penetration of solar PV and wind generation in distribution networks may change the conservation voltage reduction (CVR) capabilities. The uncertainties associated with the renewable generations and system loads are neglected in the deterministic CVR assessment. In this paper, a probabilistic framework for CVR assessment has been presented to assess the impact of uncertainties associated with renewable generations and system loads. A theoretical framework has been presented by establishing a mathematical relationship between the probability distribution of renewable generations (solar PV and wind) and the probability distribution of static exponential load model parameters. The simulation results have confirmed that the penetration of non-Gaussian solar PV and wind generation leads to non-Gaussian static exponential load model parameter distribution, which is validated by the normality tests (quantile-quantile plot, skewness, and kurtosis). Subsequently, the magnitude and probability distribution of the CVR capabilities of the network changes with the penetration of renewable generations, where the higher renewable penetration scenarios lead to higher CVR values and non-Gaussian (asymmetric) distribution.