SACRAMENTO — Gov. Jerry Brown has begun aggressively challenging federal court oversight of California’s prison system by highlighting what he says is a costly conflict of interest: The private law firms representing inmates and the judges’ own hand-picked authorities benefit financially by keeping the cases alive. How much are they making? A tally by The Associated Press, compiled from three state agencies, shows California taxpayers have spent $182 million for inmates’ attorneys and court-appointed authorities over the past 15 years. The payments cover a dozen lawsuits filed over the treatment of state prisoners, parolees and incarcerated juveniles, some of which …