This paper is devoted to true-concurrency models for probabilistic systems. By this we mean probabilistic models in which Mazurkiewicz traces, not interleavings, are given a probability. Here we address probabilistic event structures. We consider a new class of event structures, called locally finite. Locally finite event structures exhibit “finite confusion”; in particular, under some mild condition, confusion-free event structures are locally finite. In locally finite event structures, maximal configurations can be tiled with branching cells: branching cells are minimal and finite sub-structures capturing the choices performed while scanning a maximal configuration. A probabilistic event structure (p.e.s.) is a pair (E ,P), where E is a prime event structure and P is a probability on the space of maximal configurations of E . We introduce the new class of distributed probabilities for p.e.s.: distributed probabilities are such that random choices in different branching cells are performed independently in the probabilistic sense, thus ensuring that “concurrency matches probabilistic independence”. This class of p.e.s. adequately models distributed probabilistic systems with true-concurrency semantics. The results stated in this paper appeared first in the thesis  and in the conference paper .