An approach is proposed to quantify the uncertainty in probability of failure using a Gaussian process (GP) and to estimate uncertainty change before actually adding samples to GP. The approach estimates the coefficient of variation (CV) of failure probability due to prediction variance of GP. The CV is estimated using single-loop Monte Carlo simulation (MCS), which integrates the probabilistic classification function while replacing expensive multi-loop MCS. The methodology ensures a conservative estimate of CV, in order to compensate for sampling uncertainty in MCS. Uncertainty change is estimated by adding a virtual sample from the current GP and calculating the change in CV, which is called expected uncertainty change (EUC). The proposed method can help adaptive sampling schemes to determine when to stop before adding a sample. In numerical examples, the proposed method is used in conjunction with the efficient local reliability analysis to calculate the reliability of analytical function as well as the battery drop test simulation. It is shown that the EUC converges to the true uncertainty change as the model becomes accurate.