In a review of 88,000 arrestees in New York state, Carnegie Mellon University investigators found, for example, that after about 7 1/2 years the "hazard rate" for an 18-year-old first-time arrestee for robbery declined to the same rate as an 18-year-old in the general population. For 18-year-olds arrested for aggravated assault, it took about four years to reduce the risk.
For burglary, the crossover point was 3.8 years. More details here.
After these "cross over points" ex-cons who have stayed out of trouble are actually significantly less likely to be arrested than comparable members of the general public.