We explain how abstract argumentation problems can be encoded as Markov networks. From a computational perspective, this allows reducing argumentation tasks like finding labellings or deciding credulous and sceptical acceptance to probabilistic inference tasks in Markov networks. From a semantical perspective, the resulting probabilistic argumentation models are interesting in their own right. In particular, they satisfy several of the properties proposed for epistemic probabilistic argumentation by Hunter and Thimm. We also consider an extension to frameworks with deductive support and show that it maintains many of the interesting guarantees of both approaches.