This is the first lecture in the Probabilistic ML class of Prof. Dr. Philipp Hennig in the Summer Term 2020 at the University of Tübingen. Time-stamped slides available at https://uni-tuebingen.de/en/180804. Contents: * Introduction to uncertain reasoning * Kolmogorov's axioms and basic rules of probabilistic reasoning * Example uses of Bayes' Theorem Slides 4 & 13 (deductive v probabilistic reasoning) are based on prior material developed by Stefan Harmeling for a lecture course held jointly with Philipp Hennig in 2012/2013. © Philipp Hennig / University of Tübingen, 2020 CC BY-NC-SA 3.0