  Random paths are time continuous interpolations of random walks. By using
Littelmann path model, we associate to each irreducible highest weight module
of a Kac Moody algebra g a random path W. Under suitable hypotheses, we make
explicit the probability of the event E: W never exits the Weyl chamber of g.
We then give the law of the random walk defined by W conditioned by the event E
and proves this law can be recovered by applying to W the generalized Pitmann
transform introduced by Biane, Bougerol and O'Connell. This generalizes the
main results of [10] and [16] to Kac Moody root systems and arbitrary highest
weight modules. Moreover, we use here a completely new approach by exploiting
the symmetry of our construction under the action of the Weyl group of g rather
than renewal theory and Doob's theorem on Martin kernels.
