Seems that the notion of `uniformly` is the key aspect here, i.e. "the sets are ordered" in my intuitive notion.
So if the first one you've picked is red, then the only way for the next one to be green is if you started in the set of one red ball + 99 green balls; so you'd have to "pick" one specific set out of 100 possible (set of "all are green" is already impossible at this point), which is why it is very unlikely, and so you should expect the next one to be red.
And the more reds in a row you pick, the less likely you are to see a green one.
So if the first one you've picked is red, then the only way for the next one to be green is if you started in the set of one red ball + 99 green balls; so you'd have to "pick" one specific set out of 100 possible (set of "all are green" is already impossible at this point), which is why it is very unlikely, and so you should expect the next one to be red.
And the more reds in a row you pick, the less likely you are to see a green one.