  It is well known that for solutions of semi-linear parabolic PDEs, there are
equivalent probabilistic interpretations, which yields the so called nonlinear
Feymman-Kac formula. By adopting such formula, we consider in this work a novel
numerical approach for solutions of hyperbolic conservation laws. Our numerical
method consists in efficiently computing the viscosity solutions of
conservation laws. However, instead of solving the viscosity problem directly
(which is difficult), we find its equivalent probabilistic solution by adopting
the Feymman-Kac formula, which relies on solving the equivalent forward
backward stochastic differential equations. It is noticed that such framework
possesses the following advantages: (i) the viscosity parameter can be chosen
sufficiently small (say $10^{-10}$); (ii) the computational procedure on each
discretized time level can be \textit{completely parallel}; (iii) the
traditional CFL condition is dramatically weakened; (iv) one does not need to
handle the transition layers and discertizations of derivatives. Thus, high
accuracy viscosity solutions can be efficiently found. Several numerical
examples are given to demonstrate the effectiveness of the proposed numerical
method.
