probability distribution of finding a block with normalized hashrate (e.g. taking changes in pool size into account)
Sorry, it's neither hash rate nor normalization over pool size.
Of course if you're saying that the gaps are normal even if they don't look normal, then all is well in the world. Perhaps a comparison with the other pools would be more fruitful.
You are correct, what I meant was the gaps between the blocks found. But to make the comparison 'fair' the strength of the pool has to be normalized over time so you don't get peaks due to rise/fall of the pools total hashrate. Anyway, your conclusion is what I wanted to show so no harm done.