My background is in Computer Science and I'd like to establish a strong foundation in probability theory.
I was reading the GraphSLAM paper to get a sense of the algorithms used for SLAM purposes in robots. While reading it, I realized that I have a tenuous grasp on probability theory, especially on topics like covariance, conditional probability and multivariate distributions (even things like posterior probability confuse me). I've tried to search online for explanations but haven't found a single source which is both complete and comprehensive in its take. This has led to a state where I know things by name, but hardly understand them.
I'd like to rectify this and gain an intuitive understanding of the subject, since it is commonly used in numerous areas of engineering.
I dislike books that introduce fully formed theorems with no derivation or proof of how they came into existence. Which comprehensive book(s) can I read?
The book Sheldon M Ross: A First course in Probability (9th ed), Pearson (2013) seems to suit your needs.
It is highly recommended by Premium Educational Institutions for those having interest in Data Science, or having a background in Computer Science. It does have enough material to build your background as well as application-based part demanded in Computer Science.
Find it here.
You may also find this helpful, the pdf of Introduction to Probability Models by Sheldon Ross.