An easier way to think about the Raven Paradox?

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There's a famous logical paradox put forward by Carl Gustav Hempel regarding observations and logical inference.  Lets say we have some statement we're interested in like "all raven's are black".  In logical terms you could write that as "if something is a raven, then that thing is black" or "Raven → Black".  And by formal logic this is equivalent to the contrapositive statement that "if something isn't black, it's not a raven" or "not Black → not Raven".  So far so good.

But if we were to go out looking for evidence that the original statement was true then most people would readily accept that looking at a raven and finding that it's black is evidence towards the idea that all ravens are black.  But looking at instances of the contrapositive, say a white object that happens to be a rabbit it seems a bit odd to count that as evidence towards the proposition that all ravens are black, even if it's an instance of a contrapositive that's logically equivalent to the original statement.  How do rabbits relate to ravens?

To resolve this seeming paradox what works best for me is to think about how you go from evidence to proof.  To prove that "all ravens are black" by observation you would have to observe every raven and check that they are, in fact, black.  That's a bit too much work for any individual but I'm pretty sure it's within the ability of all humanity working together to find and check the color of every raven and prove that they are all black.

But to check every non-black object and see that it's not a raven?  That's not something even all of us together could do.  All the stars in the sky, all the sand grains on all the beaches, even the beaches circling those far stars.  It's just too much.  But still.  Lets say you asked a genie for help, to freeze time and to take you to every non-black object that exists.  If, at the end of all that you had found that none of those non-black objects was a raven you could then also be sure that all ravens were black, since you would have run into the counter example if it existed.  

That perfect surety comes when you've looked at every single non-black object, and looking at that very last non-black object must be evidence because it's not just evidence but proof.  But also when you're down to just a single non-black object and you haven't found any ravens yet you can still be pretty darn certain that all ravens are black, assuming that you don't have an evil genie choosing the order of objects to mess with you.

So over that absurd number of observations of non-black objects you have been accumulating evidence, just at an absurdly slow rate.  That first white rabbit you saw wasn't literally zero evidence but it is as close as makes not practical difference in any realizable situation where magical genies aren't involved.  The paradox comes with the difficulty of trying to apply our intuitions to the gap between what we reasonably call "nothing" and what is not "exactly zero".

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