How do Golomb Coded Sets work?
The data-structure is encoding a set which means it is not encoding an order.

If you draw numbers uniformly at random from some universe then sort the result (thus destroying the order information), the differences between the numbers follow an exponential distribution. The GCS uses a golomb coder to efficiently store these differences. The sort method used is irrelevant so long as its consistent with the differencing method used.

There is nothing probabilistic about the set encoding itself. But for BIP158 the set being encoded is not TXIDs but short hashes of relevant outputs. Because the hashes are short they can have collisions, making the result probabilistic.