  We study the probability of a given element, in the commutator subgroup of a
group, to be equal to a commutator of two randomly chosen group elements, and
compute explicit formulas for calculating this probability for some interesting
classes of groups having only two different conjugacy class sizes. We re-prove
the fact that if $G$ is a finite group such that the set of its conjugacy class
sizes is $\{1, p\}$, where $p$ is a prime integer, then $G$ is isoclinic (in
the sense of P. Hall) to an extraspecial $p$-group.
