  It is well-known that a quantum measurement can enhance the transition
probability between two quantum states. Such a measurement operates after
preparation of the initial state and before postselecting for the final state.
Here we analyze this kind of scenario in detail and determine which probability
distributions on a finite number of outcomes can occur for an intermediate
measurement with postselection, for given values of the following two
quantities: (i) the transition probability without measurement, (ii) the
transition probability with measurement. This is done for both the cases of
projective measurements and of generalized measurements. Among other
constraints, this quantifies a trade-off between high randomness in a
projective measurement and high measurement-modified transition probability. An
intermediate projective measurement can enhance a transition probability such
that the failure probability decreases by a factor of up to 2, but not by more.
