  We introduce the notion of a probabilistic measure which takes values in
hyperbolic numbers and which satisfies the system of axioms generalizing
directly Kolmogorov's system of axioms. We show that this new measure verifies
the usual properties of a probability; in particular, we treat the conditional
hyperbolic probability and we prove the hyperbolic analogues of the
multiplication theorem, of the law of total probability and of Bayes' theorem.
Our probability may take values which are zero--divisors and we discuss
carefully this peculiarity.
