Question on distributing weight

Question

My question is about distributing a set of non-negative weights over a set of n items, in a way that sum of weights equals 1. For example if n=2, then w1 can be some p (where p is the probability of item1, say 1/N, where N is the number of items in society where item1 comes from); and w2 is then 1-p. The question is how to advise a formula (any), when there are for example 3 or 5 items instead of 2? Thanks in advance.

Answer 1

If you have, for example, 3 items, then the probability for the items are $p_1,p_2$ and $p_3$. $p_1$ can be expressed as $p_1=1-p_2-p_3$. This condition and the condition $0 < p_i < 1 \ \forall \ i=1,2,3 $ have to be fullfilled.

If you have a uniform distribution $p_i=\frac{1}{n} \forall i=1,2,3,...,n$