From lecture notes in a course on SDE's. We are tasked with using the backward Kolmogorov equation to find.
$\mathbb{P}^{X_t=x}\left(X_T\geq2 \right)$
I am confused by the terminology here. We are looking for the probability that a process at time $t$ is equal to $x$, conditioned on the terminal value being equal to $2$. Do we then solve for the density in the backward equation and integrate over the time interval?