Combs rose from poverty in his native Clay County to earn a law degree from the University of Kentucky and open a law practice in Prestonsburg. He was decorated for prosecuting Japanese war criminals before military tribunals following World War II, then returned to Kentucky and his law practice. In 1951, Governor Lawrence Wetherby appointed him to fill a vacancy on the Kentucky Court of Appeals. Later that year, he was elected to a full term on the court, defeating former governor and judge Simeon S. Willis. Kentucky's Democratic Party had split into two factions by 1955 when Earle C. Clements, the leader of one faction, chose Combs to challenge former governor and U.S. Senator A. B. "Happy" Chandler, who headed the other, in the upcoming gubernatorial primary.