My colleague Trent Dougherty brought to me the very interesting question of how we inductively confirm that the sun will rise tomorrow given background knowledge that the sun one day won't rise.
This makes me think of an oddity. If I know that a lightbulb worked yesterday, that gives me reason to think it will work today. But if I know that it worked for the hundred preceding days, that gives me less reason to think it will work today, because it also gives me evidence that a burnout is due.
So given appropriate background knowledge—in this case, that lightbulbs burn out—more inductive cases do not necessarily raise the probability of the outcome, but can even lower it.
Burnout cases aren't the only ones like this. If I bought a lottery ticket, the more people I learn did not win, the more likely it is that I won.
Nothing greatly exciting here, except that we need to be careful to avoid flatfooted statements of how induction works.