The difference is that in that case you know the exact number of balls of each type, in this case you do not. The difference between Bernoulli and Laplace is not whether N gets bigger or smaller, but whether the number of balls is known or has to be inferred.
This is a question really, not a post, I just can't find the answer formally. Does laplace's rule of succession work when you are taking from a finite population without replacement? If I know that some papers in a hat have "yes" on them, and I know that the rest don't, and that there is a finite amount of papers, and every time I take a paper out I burn it, but I have no clue how many papers are in the hat, should I still use laplace's rule to figure out how much to expect the next paper to have a "yes" on it? or is there some adjustment you make, since every time I see a yes paper the odds of yes papers:~yes papers in the hat goes down.