(I am a newcomer in bayesian probability… so please be kind if this is very naive!)

Laplace law of succession: (r+1)/(n+2) for a binary next event

Jaynes (“Probability Theory”) appears to extend it to: (r+1)/(n+k) when the event has k possibilities.

Now suppose: you draw 4 yellow balls. Assume that you there are 1’000 color possibilities (perhaps because your colorimeter has only 3 digits).

Then the probability that the next ball is yellow would be: (4+1)/(4+1000) about 0.5%

But you can also view it this way: the ball can be either yellow or NOT yellow (any other of the 1’000 colors). Therefore since you have a binary event: yellow vs non-yellow the probability of yellow would be (4+1)/(4+2) = 5/6

This is quite different from your previous number (you could then say that the probability of a specific non-yellow color is (5/6) / 9999.

So what is really the probability of a yellow color: 0.5% or 5/6 ?