Conditional probabilities of measurements, quantum time and the Wigners friend case

Considering a minimal number of assumptions and in the context of the timeless formalism, we derive conditional probabilities for subsequent measurements in the non-relativistic regime. Only unitary transformations are considered with detection processes described by generalized measurements (POVM). One-time conditional probabilities are univocally and unambiguous derived via the Gleason-Bush theorem, also in puzzling cases like the Wigners friend scenario where their form underlines the relativity aspect of measurements. No paradoxical situations emerge and the roles of Wigner and the friend are completely interchangeable. In particular, Wigner can be seen as a superimposed of states from his/her friend.