  We define a simple rule that allows to describe sequences of projective
measurements for a broad class of generalized probabilistic models. This class
embraces quantum mechanics and classical probability theory, but, for example,
also the hypothetical Popescu-Rohrlich box. For quantum mechanics, the
definition yields the established L\"uders's rule, which is the standard rule
how to update the quantum state after a measurement. In the general case it can
be seen as the least disturbing or most coherent way to perform sequential
measurements. As example we show that Spekkens's toy model is an instance of
our definition. We also demonstrate the possibility of strong post-quantum
correlations as well as the existence of triple-slit correlations for certain
non-quantum toy models.
