The Babcockis Paradox

In probability theory, the Babcockis Paradox, or the Babcockis Effect, concerns the probability that, in a set of

n randomly chosen people in a group text of numbers one does not recognize, some set of at least 3 of them are Babcockis.

(555)555-5555: Man, who are those obnoxious guys ruining this text?
(555)555-5556: I am Babcockis.
(555)555-5557: I, too, am Babcockis!
(555)555-5558: I am Chris Burke, and therefor not Babcockis. I stood a high probabilistic chance of being Babcockis. The Babcockis Paradox states as much.
(555)555-5559: Fuck you it's Babcockis
Trey: Hey yalllll!