This article presents a concise mathematical formulation of Integrated Information Theory (IIT), aimed at making the theory more accessible. IIT is one of the most influential theories of consciousness, and from a computational point of view, it can be difficult and time-consuming to find a clear presentation of the technical details of IIT. Our presentation builds upon the work by Kleiner and Tull that presents IIT in a clear and unified mathematical framework. We propose in this paper a synthesis that highlights the core formalisms of IIT while setting aside the more philosophical aspects, such as the interpretation of IIT's axioms and postulates. The focus is squarely on the mathematical structure of IIT, utilizing basic but central concepts from probability theory, such as Markov kernels and conditional independence, to articulate how IIT formalizes consciousness. The article discusses the `cutting' of interactions within a system to isolate and evaluate its integrated information, a procedure central to IIT's procedure for quantifying consciousness. By distilling IIT to its mathematical essence, the article aims to foster broader understanding and stimulate further discussion about the theory's potential as a model for consciousness, inviting future explorations into its relationships with other theories and its implications for understanding conscious processes.