Look at the incredible luck MtRed mining pool had early on. They're likely in for a long walk of shame when few/no blocks show up for an entire difficulty tier...
If I am not mistaken bitcoin probability is independent from round to round.
You're mistaken. It doesn't matter if each round is discreet. Our probability will always reach a natural distribution.
Unless someone trapped the hashing equivalent of Maxwell's Demon inside one of their GPUs...
Yes, but it is just like rolling a die. The probability will reach a natural distribution, but just because you got three 6's in a row doesn't mean that you are more likely to go on a stretch without 6's in the future.