What is probability?

This morning, when I did my coin flipping, I got 49 heads and one edge. While this is not impossible, it's very improbable. 

There's always a struggle to interpret the fall of the coins accurately. So many decisions. The edge flip was particularly disturbing, in that it rolled for quite a while before stopping, neither falling to the head or to the tail. 

Usually, in unusual situations like this, the explanation is simple: obviously the coin isn't fair, or something is amiss with the surface it's being flipped onto, or the flipping process itself is biased, like a pitcher choosing what kind of fastball to throw. 

Moreover, there's an implicit trust in the laws of probability - is there a way they could have been suspended? Can we be sure the head and tail side of the coin remained so between the flip and the fall? Was I misreading the side it fell on when I recorded the state of the flip, adding a consciousness of Heisenbergian uncertainty in the measuring process? 

49  heads - what if I had kept going ? Would tails have come up or were they impossible? Or were they replaced with another head - magic shops sell two-headed coins after all. This isn't one of them, I checked. I'll check again.