When I look for information on mob spawning and mob grinders I find a lot of links to these two items:

The problem is, they seem to have contradictory information in them.

The first one espouses the much-credited idea that to improve your mob spawning area you must light up all the caves around it. This is built on the assumption that when the game goes to spawn a monster, it looks for an appropriate place to put one, so eliminating anywhere but your mob machine would increase the rate of mobs spawning within it.

The "Mob Spawning Science" post claims an algorithm that goes chunk by chunk, and within each chunk it picks a random block and sees if that block is a legit spawning location (standing on something, correct light level, etc.). If so, it puts a mob there. (I'm simplifying, but this is the idea.) This would imply that for any given block in a chunk, there is a 1/32768 chance of it being selected. So given a block X that is a nice, dark, mob-spawnable place, it has a 1/32768 chance each time the chunk is processed of spawning a monster regardless of any lit or unlit caves anywhere around it.

So which one is correct?