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

Probability that a given element of a group is a commutator of any two randomly chosen group elements