Riveret et al. have proposed a framework for probabilistic legal reasoning. Their goal is to determine the chance of winning a court case, given the probabilities of the judge accepting certain claimed facts and legal rules. In this paper we tackle the same problem by defining and implementing a new formalism, called probabilistic argumentation logic, which can be seen as a probabilistic generalization of Nute's defeasible logic. Not only does this provide an automation of the - only hand-performed - computations in Riveret et al, it also provides a solution to one of their open problems: a method to determine the initial probabilities from a given body of precedents.