  This note generalizes the notion of conditional probability to Riesz spaces
using the order-theoretic approach. With the aid of this concept, we establish
the law of total probability and Bayes' theorem in Riesz spaces; we also prove
an inclusion-exclusion formula in Riesz spaces. Several examples are provided
to show that the law of total probability, Bayes' theorem and
inclusion-exclusion formula in probability theory are special cases of our
results.
