What are the chances any one person would just be at all the right times in the right places, how many people on average? To secure a conviction based on just

What are the chances any one person would just be at all the right times in the right places, how many people on average? To secure a conviction based on just that, you'd want to answer "around 0.01 people" to that second question as well as prove that all of these fires were in fact arson. It would mean you get the wrong guy only every one hundred (set of) fires on average.