Discovering Probabilistic Frequent Itemsets (PFI) is very challenging since algorithms designed for deterministic data are not applicable in probabilistic data. The problem is even more difficult for probabilistic data streams where massive frequent updates need to be taken into account while respecting data stream constraints. In this paper, we propose FEMP (Fast and Exact Mining of Probabilistic data streams), the first solution for exact PFI mining in data streams with sliding windows. FEMP allows updating the frequentness probability of an itemset whenever a transaction is added or removed from the observation window. Using these update operations, we are able to extract PFI in sliding windows with very low response times. Furthermore, our method is exact, meaning that we are able to discover the exact probabilistic frequentness distribution function for any monitored itemset, at any time. We implemented FEMP and conducted an extensive experimental evaluation over synthetic and real-world data sets; the results illustrate its very good performance.