Here's one hint from Al Jazeera of how the FBI got involved:

NBC News reported on its website on Friday, quoting US law-enforcement officials, that (Paula) Broadwell was under FBI investigation for improperly trying to access Petraeus' email and possibly gaining access to classified information. Broadwell had extensive access to Petraeus in Afghanistan and has given numerous television interviews speaking about him, the report said.

Charley Noble