Logical methods for modeling human reasoning have been developed to the stage where manyformal models are available. However, research focusing on applying them to real domains isscarce. Often, it is not clear which of the many formal tools is suitable for a given application, ifany. Few applications of those formal tools would be considered useful by people working in thosereal domains. My proposal aims to improve this situation, by assessing and developing varioususes of mathematical methods to model probabilistic reasoning in the real-life context of judicialand forensic justifications.The objectives of this proposal are: [1] to determine which mathematical and logical probabilistictools best fit the forensic and judicial notion of probability, [2] to develop and examine forensicand judicial uses of such tools and [3] to investigate the extent to which lessons learned in suchcontexts carry over to other applications of probability apparatus.The novelty of the approach consists in focusing on real-life cases and attempting to work outtechnical apparatus that actually fits them. The main risk is that idealized mathematical toolsmight turn out to be too abstract or computationally too complex to adequately capture themessy details of real-life considerations. The challenge will be to develop them avoiding suchproblems.