In the probabilistic simulations, the main aim is to search the output distribution for the given range of input uncertainties. The problem is that the simulated output distribution can be the result of uncertainties other than the input uncertainties. In deterministic analysis, the output distribution is the result of input uncertainty and modelling uncertainty. Whereas in stochastic analysis the output distribution is the result of input uncertainty, modelling uncertainty and sampling uncertainty. How these uncertainty types combine in the context of reliability analyses is not well understood. In this work, using arbitrary examples, we present the connection between various uncertainties involved in the probabilistic simulations. We study how the modelling and sampling uncertainty propagates to the predicted output distributions. We also propose a simple uncertainty model helpful for the quantification and treatment of modelling uncertainties in the probabilistic simulations. The proposed correction method is shown to improve the accuracy of the output distributions. In practical applications, this would lead to more accurate estimates of failure probabilities.