  The possibility to recover the which-way information, for example in the two
slit experiment, is based on a natural but implicit assumption about the
position of a particle {\it before} a position measurement is performed on it.
This assumption cannot be deduced from the standard postulates of quantum
mechanics. In the present paper this assumption is made explicit and formally
postulated as a new rule, the {\it quantum typicality rule}. This rule
correlates the positions of the particles at two different times, thus defining
their trajectories. Unexpectedly, this rule is also equivalent to the Born rule
with regard to the explanation of the results of statistical experiments. For
this reason it can be considered a generalization of the Born rule. The
existence of the quantum typicality rule strongly suggests the possibility of a
new trajectory-based formulation of quantum mechanics. According to this new
formulation, a closed quantum system is represented as a {\it quantum process},
which corresponds to a canonical stochastic process in which the probability
measure is replaced by the wave function and the usual frequentist
interpretation of probability is replaced by the quantum typicality rule.
