Alice has chosen a password $p\in P$ in the password space $P$. Let's assume that $\Pr_P(p) = 1/|P|$. If Alice employs a password system due to regular password changes, she chooses the new password $p'$.
While $\Pr_P(p) = \Pr_P(p')$ might hold true, $\Pr_P(p'|p)$ will be close to zero.
This isn't at all worked through right now, it's just the sketch of an idea. It's probably better to reason informally on this one.
Alice has chosen a password $p\in P$ in the password space $P$. Let's assume that $\Pr_P(p) = 1/|P|$. If Alice employs a password system due to regular password changes, she chooses the new password $p'$.
While $\Pr_P(p) = \Pr_P(p')$ might hold true, $\Pr_P(p'|p)$ will be close to zero.
This isn't at all worked through right now, it's just the sketch of an idea. It's probably better to reason informally on this one.