The comment in this question establishes that when part of a sample space is considered to no longer be possible, how the eliminated probabilities are redistributed to the remaining sample space is uniquely mathematically determined.
Why is this the case? Does it follow from the Kolmogorov axioms? What is the mathematical argument that there is there no philosophical latitude available to shape the new probability distribution?
Edit So if we have a random variable $A$ which can take values in $\Omega = \{1,\ 2,\ 3\}$, and $B \subset \Omega$ is the event that $A \neq 3$, I'm interested in being shown why the way $\Pr(A\ |\ B)$ redistributes between $\Pr(A = 1)$ and $\Pr(A = 2)$ the probability mass that initially belonged to $B^C$ must be unique, even in the absence of a physical reason (such as with dice, where it is physically obvious that $\Pr(A = 1)$ must equal $\Pr(A = 2)$ in both $\Omega$ and $B$).