A single-domain nanomagnet is a basic example of system where relaxation
from high to low energy is probabilistic in nature even when thermal
fluctuations are neglected. The reason is the presence of multiple stable
states combined with extreme sensitivity to initial conditions. It is
demonstrated that for this system the probability of relaxing from high
energies to one of the stable magnetization orientations can be tuned to
whatever desired value between 0 and 1 by applying a small transverse
magnetic field of appropriate amplitude. In particular, exact analytical
predictions are derived for the conditions under which the probability of
reaching one of the stable states becomes exactly 0 or 1. Under these
conditions, magnetization relaxation is totally insensitive to initial
conditions and the final state can be predicted with certainty. This
conclusion implies that any attempt to regularise the dynamics by taking
the limit of dissipation constant going to zero will fail because this
limit does not exist, except for highly non-generic field conditions.