You are not more likely to arrive at one of the smaller gaps because there are more of them; you seem to think that there is some sort of urn from which you are drawing out gaps of time with equal probability; easy mistake to make. Think of it this way; you are minutes from an urn, numbered :00-:59. There is one 45 minute gap and 15 one -minute gaps. You are most likely to pick a minute belonging to the 45 minute gap.

Additionally, what he says doesn't apply to all non-uniform distributions, but only to those where the times between buses are exponentially distributed (and thus memoryless)

You are not more likely to arrive at one of the smaller gaps because there are more of them; you seem to think that there is some sort of urn from which you are drawing out gaps of time with equal probability; easy mistake to make. Think of it this way; you are minutes from an urn, numbered :00-:59. There is one 45 minute gap and 15 one -minute gaps. You are most likely to pick a minute belonging to the 45 minute gap.

Additionally, what he says doesn't apply to all non-uniform distributions, but only to those where the times between buses are exponentially distributed (and thus memoryless)