Markov categories are the central framework for categorical probability theory. Many important concepts from probability theory can be formalized in a Markov category. In particular, conditional probability distributions and Bayes’ theorem are captured via the notion of conditionals in a Markov category. Gaussian probability theory gives an example of a Markov category with conditionals, where the conditionals can be computed using the Moore-Penrose inverse. In this talk, I will explain how to generalize this example by providing a construction on a Moore-Penrose dagger additive category which produces a Markov category with conditionals. Applying this construction to the category of real matrices gives us back the Gaussian probability theory example.