Which of the 2 examples ? In the first case an innocentman was executed. In both cases a trial jury found the defendant guilty, so there was apparently no doubt, at least 'beyond any reasonable...', at that point. Who draws the line ? Who verifies that sufficient evidence has been supplied to ensure that there is 'no doubt at all' ? Define 'no doubt at all'. There are a multitude of cases where people have been found guilty, and only after serving many years inside, ( those lucky enough not to have been hanged that is ), has a Miscarriage of Justice been shown to have occurred:
http://www.innocent.org.uk/cases/