  Neglecting many motivating details for the Park-Pham theorem (previously
known as the Kahn-Kalai conjecture), the result starts with a finite set $X$, a
non-trivial upper set $\mathcal{F} \subseteq 2^X$, and a particular
parameterized family of random variables $X_p$, then proceeds to provide an
upper bound on the value $p_c(\mathcal{F})$ such that
$\mathbb{P}(X_{p_c(\mathcal{F})} \in \mathcal{F}) = 1/2$. A natural question to
ask is if there is an analog to the Park-Pham theorem for upper sets in finite
posets other than $2^X$ and other parameterized families of random variables
taking values in them. In this short note, we show that there is, with minor
adjustments, in at least one circumstance. This is done by producing a
conditional version of the $\epsilon$-dependent form of the Park-Pham theorem,
which may be interesting in its own right.
