> If every time you enter the legal system and you have a 1% chance of being falsely convicted

I agree with you that 1% is a high number in this context, but I don't think the math works for what you're saying here.

If 1 out of 100 convictions are of innocent people, that doesn't mean that 1 out of 100 innocent people put on trial are going to get convicted. That rate could be higher or lower than 1% because it depends how many innocent people are rightfully judged innocent.

Hypothetically, a court system that always returns a guilty verdict could have a 1% false conviction rate if 99% of people put on trial are actually guilty. But the rate of wrongful conviction for an innocent person entering this system would be 100%.