I think you're misunderstanding probability theory a little. Probability theory is the chance that x result means that the universe operates on principle y. The fact that the second researcher had no reason to stop until he tested 100 people means that the % of patients cured did not exceed 60% until his last batch of test subjects. Which significantly alters the chance that the universe operates on principle y. The first researcher could have had a % over 60 at any time during the experiment. Which is a physical difference. The probability used is not based on the researcher's private thoughts, it is based on their experimental procedure, which is different, regardless of the fact they ended with the same results.