The complexity of modern computer and software systems still seems to grow exponentially, while the human user is widely left without explanations on how to understand these systems. One of the central tasks of current computer science therefore lies in the development of methods and tools to build such an understanding. A similar task is addressed by formal verification which gives various verifiable justifications for the functionality of a system. As these still only give knowledge that a system functions properly they only address a portion of the task to make systems easier to comprehend. It is widely believed that cause-effect reasoning plays an important role in forming human understanding of complex relations. Thus, there are already many accounts on causality in modern computer science. However, most of them are focusing on a form of backward looking actual causality. This variant of causality is concerned with actual events after their occurrence and tries to reason about causes mostly in a counterfactual manner. In this thesis we address a probabilistic form of causality which is forward looking by nature. As such, we define and discuss novel notions of probabilistic causes in discrete time Markov chains and Markov decision processes. For this we rely on two central principles of probabilistic causality. On one hand, the probability-raising principle states that a cause should raise the probability of its effect. On the other hand, temporal priority requires that a cause must occur before its effect. We build the mathematical and algorithmic foundations of our so called probability-raising causes. For this we work in a state-based setting where causes and effects are reachability properties of sets of states. In order to measure the predictive power of states we define quality-measures for which we interpret causes as binary classifiers. With these tools we address the algorithmic questions of checking cause-effect relations if both a cause candidate and an effect are given and finding quality-optimal causes if only the effect is given. We discuss possible extensions of this basic state-based framework to more general formulations of causes and effects as ω-regular properties.