  The short time behavior of nucleation probabilities is studied by
representing nucleation as diffusion in a potential well with escape over a
barrier. If initially all growing nuclei start at the bottom of the well, the
first nucleation time on average is larger than the inverse nucleation
frequency. Explicit expressions are obtained for the short time probability of
first nucleation. For very short times these become independent of the shape of
the potential well. They agree well with numerical results from an exact
enumeration scheme. For a large number N of growing nuclei the average first
nucleation time scales as 1/\log N in contrast to the long-time nucleation
frequency, which scales as 1/N. For linear potential wells closed form
expressions are obtained for all times.
