Most of what this chapter reviews is genuinely review: random variables, joint distributions, and Bayes' theorem all come straight from the probability course, revisited here only to have them fresh before Chapter 1 leans on them immediately.
Two pieces are new, though, and they aren't a light touch — they're the actual mathematical engine behind nearly every theorem in this course. How a function bends, and what that bending guarantees about averages versus applying the function first, is what makes entropy provably non-negative, proves that averaging two distributions can't decrease entropy, and shows that relative entropy is never negative. Markov chains and their stationary distributions are what let Chapter 8 define a well-behaved notion of "entropy per symbol" for a source whose symbols depend on each other, not just an idealized independent stream.
The chapter closes by asking a question that sounds almost philosophical — why does information have to be measured with a logarithm at all? — and answers it directly: a logarithm isn't a stylistic choice, it's forced by requiring that learning two independent things gives exactly as much information as learning each one separately.
By the end, every tool Chapter 1 needs to define information itself will already be in hand.