Magic in my pocket

Each time I approach my lab door in the morning, I feel touched by mystery. But this has nothing to do with the tantalizing questions waiting for me behind that door, but with the task to unlock it. There are seven keys in my pocket, held together by a ring. Only one of them is the right one. Two of them are on first glance indistinguishable from each other, and unfortunately I need exactly one of those.
Of course there must be subtle differences in the fine structure of the bit, and maybe I should rather concentrate on that; but up to now I prefer the numbers. Four digits are engraved in each of the two keys, and the last one differs. To unlock my lab door, I need the key with the digit 3 at the end; the other with the digit 1 would not work. Therefore, while I'm getting near my door, I fumble the keys out of my pocket and try to make out these last digits.
And that's when mystery sets in. I can see the keys in my hand, and I don't need much inspection to discover those two ones with the digits 1 or 3. But I must look closer to see the digits. Usually, I stick my finger through the ring and produce one of the two keys at the front. Just before I recognize its digit (at the end of four), it could be the right or it could be the wrong one. The chances are 50:50.
I perfectly know: the numbers are there also before I look closely. But are they? Aren't they just two possibilities of equal probability? From a distance, both keys look the same to me. I couldn't tell them from each other. They are 'these two keys', patiently waiting for my further distinction. I imagine the last digit of their engraved numbers flipping between one and three - or rather being stuck somewhere between, undecided.
Only on closer inspection the key that by chance came in front of the others on the palm of my hand reveals its identity, at the same time revealing the identity of its nearly identical twin. Thus, I always make two discoveries at once: The digit on the key proves its identity to me once I see it, and simultaneously the identity of the key that I can't see. The first discovery is based on evidence, the second on my prior knowledge.
The positions of the two keys relative to each other before I take them out of my pocket is totally unknown. Neither me nor anybody else can have any idea of it. The keys even could be silver, could be gold, could shine in fancy colours, with greek signs engraved on them, with changing symbols of magic. I wouldn't know. But nevertheless, I claim to know the number on the second key once I see the first. Why?
Why am I so sure? I own these keys now for almost one year, but only recently I use them regularly. Maybe 30 or 40 times I had to find the right one. Up to now it never happened that both keys had the same number.  Are 30-40 repetitions with identical results sufficient for certainty? Shouldn't I wait for more repetitions before drawing definite conclusions?
Not necessarily. I guess my confidence is based on much more than just 30-40 repetitions. The two keys are just an example for a more general principle. In fact, each day of my life has confronted me with numerous similar experiences. My experiment with the keys is just the last in a long chain of similar experiments. And the overwhelming majority of the results came out straight, with things keeping their identity.
And for the same reasons I don't believe in fancy colours and magical signs in my pocket, while I'm not looking.
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On the border between fiction and reality