Scott Aaronson's introduction of Quantum Theory as "a certain generalization of probability theory" is very nice and to the point.

(Further Reading)

These notes of Greg Kuperberg are more accessible than Caves, Fuchs, and Schack (at least for me):

"An introduction to quantum probability, quantum mechanics, and quantum computation"

https://www.math.ucdavis.edu/~greg/intro.pdf