There’s an old joke that “there are no guilty men in prison,” i.e. that practically all inmates claim to have been unjustly accused. I’ve also heard that in fact most convicts cheerfully admit to the charges. The latter seems more likely given that reporters find it worth mentioning that so-and-so (e.g. the late Tookie) “has always maintained his innocence”.
I recently found (but did not save the address of) a website listing the last words of convicts put to death in Texas. I read the most recent dozen or so. Almost half expressed remorse, and just one expressed a hope that the real criminal would someday be found.