This work deals with explainable artificial intelligence (XAI), specifically focusing on improving the intelligibility of decision trees through reliable and concise probabilistic explanations. Decision trees are popular because they are considered highly interpretable. Due to cognitive limitations, abductive explanations can be too large to be interpretable by human users. When this happens, decision trees are far from being easily interpretable. In this context, our goal is to enhance the intelligibility of decision trees by using probabilistic explanations. Drawing inspiration from previous work on approximating probabilistic explanations, we propose a greedy algorithm that enables us to derive concise and reliable probabilistic explanations for decision trees. We provide a detailed description of this algorithm and compare it to the state-of-the-art SAT encoding. In the order to highlight the gains in intelligibility while emphasizing its empirical effectiveness, we will conduct in-depth experiments on binary decision trees as well as on cases of multi-class classification. We expect significant gains in intelligibility. Finally, to demonstrate the usefulness of such an approach in a practical context, we chose to carry out additional experiments focused on text classification, in particular the detection of emotions in tweets. Our objective is to determine the set of words explaining the emotion predicted by the decision tree.