It's going to apply to anything that has a probability distribution that is monotonically decreasing at any rate, exponential or not.

This is pretty obvious: the probability of the number 1 will be greater than the number 2, and so on up to 9.

The probability of the range 10-19 will be greater than the range 20-29, and so on.

The probability of the range 100-199 will be greater than the range 200-299, and so on.

And so on... The probability of the ranges starting with "1" will always be higher.

Also, I have no idea why anyone would think this is "arcane". It's very simple and obvious and a good example of where intuition can go wrong.