This paper presents a probabilistic generalization of the Generalized Optimal Sub-Pattern Assignment (GOSPA) metric, termed P-GOSPA. The GOSPA metric has been widely used to evaluate the distance between finite sets, particularly in multi-object estimation applications. The P-GOSPA extends GOSPA into the space of multi-Bernoulli densities, incorporating inherent uncertainty in probabilistic multi-object representations. Additionally, P-GOSPA retains the interpretability of GOSPA, such as its decomposition into localization, missed detection, and false detection errors in a sound and meaningful manner. Examples and simulations are provided to demonstrate the efficacy of the proposed P-GOSPA metric.