The collapse of the dazzling career of CIA Director David H. Petraeus was triggered when a woman with whom he was having an affair sent threatening e-mails to another woman close to him, according to three senior law enforcement officials with knowledge of the episode. The recipient of the e-mails was so frightened that she went to the FBI for protection and help tracking down the sender, according to the officials. The FBI investigation traced the threats to Paula Broadwell, a former military officer and a Petraeus biographer, and uncovered explicit e-mails between Broadwell and Petraeus, the officials said.