Okay, so this article explains more about the start of the investigation. I can understand the rigor to which the FBI pursued the emails.

(Open Source) After Kelley alerted the FBI, agents began pursuing it as a possible case of cyber harassment or stalking. “The thought was she was being followed,” the source said.

The anonymous emails continued — sent from multiple alias accounts — and some later ones in the sequence contained references to Petraeus, though not by name, the source said.

What most alarmed Kelley and the FBI, the source said, were references to “the comings and goings” of high-level generals from the U.S. Central Command, which is based at MacDill Air Force Base in Tampa, and the U.S. Southern Command, as well as Petraeus — including events that were not on any public schedule. This raised the question as to whether somebody had access to sensitive — and classified — information.

Moreover, the sender of the emails had “covered her tracks pretty well,” the source said.

However, once it was determined that no laws were broken, why did the investigation then continue? Because to see if Petraeus was behind the emails is lame beyond all belief. And makes absolutely no sense.

Other post about this subject: In case anyone is wondering; Rove Once Again Leaking CIA Info? What Happened?