If you already know analysis (well), the best probability book is "Probability & Measure" by Billingsley. A gentler introduction is the SUMS book "Measure, Prob

If you already know analysis (well), the best probability book is "Probability & Measure" by Billingsley. A gentler introduction is the SUMS book "Measure, Probability, and Integral." If you don't care about measure theory and just want to learn how to calculate the probability that a coin comes up heads in the first five attempts, the book by Larsen and Marx is pretty good.