  A recent description of diffusion-limited nucleation based on fluctuating
hydrodynamics that extends classical nucleation theory predicts a very
non-classical two-step scenario whereby nucleation is most likely to occur in
spatially-extended, low-amplitude density fluctuations. In this paper, it is
shown how the formalism can be used to determine the maximum probability of
observing \emph{any} proposed nucleation pathway, thus allowing one to address
the question as to their relative likelihood, including of the newly proposed
pathway compared to classical scenarios. Calculations are presented for the
nucleation of high-concentration bubbles in a low-concentration solution of
globular proteins and it is found that the relative probabilities (new theory
compared to classical result) for reaching a critical nucleus containing $N_c$
molecules scales as $e^{-N_c/3}$ thus indicating that for all but the smallest
nuclei, the classical scenario is extremely unlikely.
