  The quantum measurement problem can be regarded as the tension between the
two alternative dynamics prescribed by quantum mechanics: the unitary evolution
of the wave function and the state-update rule (or "collapse") at the instant a
measurement takes place. The notorious Wigner's friend gedankenexperiment
constitutes the paradoxical scenario in which different observers (one of whom
is observed by the other) describe one and the same interaction differently,
one --the Friend-- via state-update and the other --Wigner-- unitarily. This
can lead to Wigner and his friend assigning different probabilities to the
outcome of the same subsequent measurement. In this paper, we apply the
Page-Wootters mechanism (PWM) as a timeless description of Wigner's friend-like
scenarios. We show that the standard rules to assign two-time conditional
probabilities within the PWM need to be modified to deal with the Wigner's
friend gedankenexperiment. We identify three main definitions of such modified
rules to assign two-time conditional probabilities, all of which reduce to
standard quantum theory for non-Wigner's friend scenarios. However, when
applied to the Wigner's friend setup each rule assigns different conditional
probabilities, potentially resolving the probability-assignment paradox in a
different manner. Moreover, one rule imposes strict limits on when a joint
probability distribution for the measurement outcomes of Wigner and his Friend
is well-defined, which single out those cases where Wigner's measurement does
not disturb the Friend's memory and such a probability has an operational
meaning in terms of collectible statistics. Interestingly, the same limits
guarantee that said measurement outcomes fulfill the consistency condition of
the consistent histories framework.
