The assumption is worked in. He assumes a base rate of only 0.1% of all cars are blue, and then shows that even with this it is astronomically unlikely the car isn't blue. He could have explicitly calculated how low a base rate you'd need for, say, a 50% chance the car is blue, and that number would be astronomically small as well.
While working the numbers was needed for the SE answer, I actually think it obscures the intuition.
The high order bit here is that there's only a 10% chance of a false positive, and so you're raising 0.1 to the 900th power. Everything else is a second order term relative to that, and you can instantly see the answer will be "nearly certain".
The answer calculates a likelihood ratio of 10^763, so for a 50% chance you'd need a prior probability of less than 1/(10^763 - 1) ≈ 10^(-763), which would imply that there is most likely not a single blue car in the universe.
While working the numbers was needed for the SE answer, I actually think it obscures the intuition.
The high order bit here is that there's only a 10% chance of a false positive, and so you're raising 0.1 to the 900th power. Everything else is a second order term relative to that, and you can instantly see the answer will be "nearly certain".