By their very nature, rare event probabilities are expensive to compute; they are also delicate to estimate as their value strongly depends on distributional assumptions on the model parameters. Hence, understanding the sensitivity of the computed rare event probabilities to the hyperparameters that define the distribution law of the model parameters is crucial. We show that by (i) accelerating the calculation of rare event probabilities through subset simulation and (ii) approximating the resulting probabilities through a polynomial chaos expansion, the global sensitivity of such problems can be analyzed through a double-loop sampling approach. The resulting method is conceptually simple and computationally efficient. We demonstrate the efficiency of this method on an analytical example and an application from subsurface flow.