No, not quite. The probability that this is not a coincidence is unknown. The probability that you SAW the data if the particle didn't exist is 100%. The proba

No, not quite. The probability that this is not a coincidence is unknown. The probability that you SAW the data if the particle didn't exist is 100%. The probability that you will not see it /again/ is 999/1000. The probabilities 1/1000 (or 999/1000) are only meaningul probabilites for something in the world where in fact it was a coincidence. In any other world, they are not. So saying "there is a 999/1000 chance that this is not a coincidence" isn't true, as the calculation of 999/1000 must assume that it fact it IS a coincidence.