Similar problem which ends up not being quite as simple in the general case as you might think: sampling from a unit simplex: http://www.cs.cmu.edu/~nasmith/pap

Similar problem which ends up not being quite as simple in the general case as you might think: sampling from a unit simplex: http://www.cs.cmu.edu/~nasmith/papers/smith+tromble.tr04.pdf http://www.cs.cmu.edu/~nasmith/papers/smith+tromble.tr04.pdf