We consider a distributed labeled multi-Bernoulli (LMB) filter that uses the generalized covariance intersection technique for fusing the local LMB distributions. A critical aspect of such filters is to correctly associate labeled Bernoulli components describing the same object at different sensors. Here, we improve on previously proposed association schemes by introducing a probabilistic framework and algorithm for object (label) association. Instead of enforcing a hard association, we propose to compute association probabilities and use them in the fusion of the LMB posterior distributions. To develop our probabilistic label association scheme, we first derive a formulation of the fused multiobject distribution that involves a label association distribution. We then show that approximating the label association distribution by the product of its marginals results in a fused multiobject distribution that is again of LMB type. An efficient LMB fusion algorithm is finally obtained by using a belief propagation scheme for fast approximate marginalization and a Gaussian approximation. Simulation results demonstrate that the resulting distributed LMB filter outperforms a state-of-the-art method using hard label association.