PORTLAND — The breakthrough in the 9-year-old mystery surrounding the killing of a prominent federal public defender came after the suspect talked about the crime and someone tipped off investigators. Prosecutors and police haven’t disclosed what led to the arrest of 28-year-old Christopher Alexander Williamson in the Nov. 24, 2009, strangulation of Assistant Federal Public Defender Nancy Bergeson. But others close to the investigation said it was a combination of tenacity by detectives, the suspect’s loose lips years after the crime and some luck. Court records show Williamson lived at two addresses near Bergeson in Southwest Portland at the time, including one about two miles away.