Suppose that the vector $\tilde{a} = (a_1,a_2,...,a_J)$ has a multivariate normal distribution and let $$A = \Sigma_{j=1}^J a_j\,.$$
Then what is the distribution of $a_j/A$ or $\tilde{a}/A$ called?
I do know that Dirichlet distribution can be used to deal with a vector of which the sum of the elements is one, but I'm asking the special case where the vector has a multivariate Normal distribution.