  It is shown that a normalisable probability density can be defined for the
entire complex plane in the modified de Broglie-Bohm quantum mechanics, which
gives complex quantum trajectories. This work is in continuation of a previous
one that defined a conserved probability for most of the regions in the complex
space in terms of a trajectory integral, indicating a dynamical origin of
quantum probability. There it was also shown that the quantum trajectories
obtained are the same characteristic curves that propagate information about
the conserved probability density. Though the probability density we now adopt
for those regions left out in the previous work is not conserved locally, the
net source of probability for such regions is seen to be zero in the example
considered, allowing to make the total probability conserved. The new combined
probability density agrees with the Born's probability everywhere on the real
line, as required. A major fall out of the present scheme is that it explains
why in the classical limit the imaginary parts of trajectories are not observed
even indirectly and particles are confined close to the real line.
