Punishments get scaled by the judged likelihood of guilt, i.e. judge says there's a 65% chance Bill is the killer, Bill gets 65% of the punishment.

For this to accommodate anything vaguely comparable to our current concept of "innocent until proven guilty," it'd need to be something like the probability to the third or fourth power (or conceivably higher). If a hundred people were charged with murder and convicted under this standard, you'd be sending 35 innocent guys to jail for 20-40 years. If it were, say, 20%, you'd be sending 80 innocent guys to jail for about 8-10 years. Consider that currently someone is acquitted if the evidence is short of somewhere in the 95%+ range, this would lead to a vast, vast increase in the false positive amount, which is probably already somewhat high. It would, admittedly, also increase the rightfully convicted, but given our current laws, I'm not sure that's an all-out plus.