My question is general, but is in reference to this popular question: Probability that n points on a circle are in one semicircle
In the answer of this question, we label the points clockwise from 1 to n. However, in reality when we are doing the experiment we would up with points that are not sorted clockwise (we would sample points sequentially). We can argue that we can simply swap the labelling to get sorted points, but then aren't we changing the outcome of the experiment? Is it something like, we can only restrict labels to a subset of the probability space when each outcome is equally likely?
Can't quite get my head to wrap around this.
