Let $P$ be a probability distribution over a finite Boolean algebra $\mathfrak{B}$, and fix a parameter $t_{P} \in (\frac{2}{3}, 1)$. Define the `revision function of $P$', $R_{P}: \mathfrak{B}\setminus\{\bot\} \rightarrow \mathbb{P}(\mathfrak{B})$ as follows, (assuming that $P$ assigns positive probability to all events other than the null event $\bot$)

$$R_{P}(X) = \{Y \in \mathfrak{B}|P(Y|X) \geq t\}.$$

In words, the revision function of $P$ takes an event $X$ in $\mathfrak{B}$ and returns the set of all events whose conditional probability given $X$ (according to $P$) is at least $t$. 

I want to find a way of constructing, for any given $P$ and any $t_{P} \in (\frac{2}{3}, 1)$, another probability function $P^{*}$ with a corresponding parameter $t_{P^{*}} \in (\frac{2}{3}, 1)$ such that $R_{P^{*}} = R_{P}$. In other words, given any probability function and fixed parameter in the specified range, I want a method for constructing another function that (for some choice of parameter in the specified range) gives rise to the same revision function as the original function.