Discontinuous term of the distribution for Markovian random evolution in $\mathrm R^3$

We consider the random motion at constant finite speed in the space $R^3$ subject to the control of a homogeneous Poisson process and with uniform choice of directions on the unit 3-sphere. We obtain the explicit forms of the conditional characteristic function and conditional distribution when one change of direction occurs. We show that this conditional distribution represents a discontinuous term of the transition function of the motion.