So, what are the odds? Does a statistical improbability prove anything? I say "No!" Not only that, in many cases the highly improbable is the most likely outcome. If you're looking for your own impossible event, they're actually quite easy to create...
Here is a simple experiment. Go to your game room / kitchen junk draw / where-ever, and get a deck of cards. OK, now... shuffle them and write down the sequence of cards you produced. Viola! No matter what sequence you wrote, that sequence had approximately a 1 in 8x10^67 probability of occurring. That is an 8 followed by 67 zeros. Is it a miracle? Does it prove anything? Shuffle the deck again and then write down the new sequence right after the previous sequence so you now have 104 card numbers in a row. Whatever your outcome, that sequence has a probability of 8x10^67 times 8x10^67, or 6.4x10^4490. That is 6.4 followed by 4490 zeros! Does it prove anything? With a simple deck of cards, you can produce an event as unlikely as you want, all you need to do is keep shuffling and recording the outcome.
Lets look at it from a different angle. Shuffle the deck, write down the numbers, then shuffle it again. What are the odds that "Nothing Happened"? If "Nothing Happened" means that the new sequence after the shuffle is exactly the same as the old sequence, then the odds of "Nothing Happened" is about 1 in 8x10^67. So, the odds of "Nothing Happening" is near zero, and the odds of an "Impossible Event" occurring is a near certainty. So now the impossible is normal.
Here is another fun one: what are the odds you can shuffle the deck and produce a "Perfectly Ordered Set"? By this, I mean cards order Ace-King in suit and in sequence of hearts, spades, diamonds, then clubs. Well, the odds are damn near 100%, it is just a matter of how fast you shuffle and how long you are willing to wait.
If you aren't willing to wait, lets speed this up. Lets replace the normal deck with a set of sticky cards. Now these cards are sticky in a special way: a 2 sticks on top of an ace of the same suit, a 3 sticks to a 2 in a similar manner, and so on such that each card sticks to its one-lower card of the same suit. And, the ace of spades sticks to the king of hearts, the ace of diamonds sticks to the king of spades, and the ace of clubs sticks to the king of diamonds. Now how many times do you have to shuffle before you get a perfectly order set? I haven't run the odds, but my guess is a couple hundred of shuffles should do it (maybe Nate can figure this one out?). Not only that, once you get the perfectly ordered set, the system stops changing. If you missed the initial shuffling, you'd think the perfectly ordered set existed forever. This is called an "Attractor", in this case there is only one and it is static.
We can add more attractors by adding rule. Lets allow cards to stack on-top or below their adjacent card. Now we shuffle and shuffle and ultimately end up with a clumpy deck of cards stuck in groups and no free cards (top or bottom of a clump) able to stick to any other free cards. If we reset the deck and shuffle again, we get a different but similar outcome, cards clumped together. Now we have lots of attractors, but they are all static.
OK, so this is a cheap example. You can shuffle until you are blue in the face, but all you end up with is various card sequences, not a frog. Well, there aren't any frogs made of cards running around. But, lets get a little more creative, lets throw out the royalty and stick to ace through ten. Lets redefine 'sticky' as magic sums ending in 2, 8, or 0 (10). So, if any group of cards next to each other, when added together produce a 2, 8, or 0 in their last digit, they stick. Now we can shuffle and produce water (8+Ace+Ace), carbon-dioxide (6+8+8), and a few other elementary compounds. Neon (10), doesn't mix and is an inert gas, er card.
Now lets expand the deck to represent all of the atoms that make up the earth. Lets makes the "rules of stickiness" the rules of chemical attraction. Lets shuffle it by having the sun rise and heat things up, then set and let things cool off. Lets throw in annual seasons, rain and wind, thunder and lightning, volcanoes, and everything else that is going on. Lets repeat this shuffling for 4 billion years. I didn't mention it, but throw in cyclical attractors – cycles that repeat through a set of states (a static attractor has only 1 state). Now, what are the odds that nothing will happen?