So you're watching some TV and you get the munchies for a cheese sandwich. You could sit there trying work out if there's any cheddar left in your fridge, perhaps trying to recall when you last bought any and how much has been eaten since then. Or, you could get off your ass, open the fridge and have a look.
If you don't see any cheese after a cursory look, you could empty the fridge to make a thorough examination. Damn! There's no cheese!
Your absence of evidence is clear evidence of absence. In fact, in this sort of situation it is difficult to imagine what other evidence would suffice to prove that there is no cheese sandwich coming your way.
So you're sitting there wondering if God exists . . . . .