Predicting the next action that a human is most likely to perform is key to human-AI collaboration and has consequently attracted increasing research interests in recent years. An important factor for next action prediction are human intentions: If the AI agent knows the intention it can predict future actions and plan collaboration more effectively. Existing Bayesian methods for this task struggle with complex visual input while deep neural network (DNN) based methods do not provide uncertainty quantifications. In this work we combine both approaches for the first time and show that the predicted next action probabilities contain information that can be used to infer the underlying intention. We propose a two-step approach to human intention prediction: While a DNN predicts the probabilities of the next action, MCMC-based Bayesian inference is used to infer the underlying intention from these predictions. This approach not only allows for independent design of the DNN architecture but also the subsequently fast, design-independent inference of human intentions. We evaluate our method using a series of experiments on the Watch-And-Help (WAH) and a keyboard and mouse interaction dataset. Our results show that our approach can accurately predict human intentions from observed actions and the implicit information contained in next action probabilities. Furthermore, we show that our approach can predict the correct intention even if only few actions have been observed.