Fokker-Planck confusion

Question

So, I understand that solving the Fokker-Planck / Kolmogorov Forward equation gives the time-dependent probability density $p(x,t)$ in 1-D let's say.

My question is, how do you use this? Let's say, I wanted to find the probability of a particle being at a position $x = a$, at time $t = \tau$, how would you calculate this from $p(x,t)$?

Thanks!

Answer 1

It should be $0$, for a specific $x$.

But you can find the probability that the particle will be located in $[a-\delta/2;a+\delta/2]$ by integrating the equation.