  Prediction of nucleation rates in first order phase transitions requires the
knowledge of the barrier associated to the free energy profile $W$. Molecular
simulations offer a direct route through $W = -kT \ln p_a$, where $k$ is
Boltzmann's constant, $T$ is temperature, and $p_a$ the probability
distribution of the size of any nucleus. But in practice, the extremely scarce
spontaneous occurrence of large nuclei impedes the full determination of $p_a$,
and a numerical bias must be introduced, e.g. on the size of the largest
nucleus in the system, leading to the probability size distribution of the
largest nucleus $p_l$. Although $p_l$ is known to be system size dependent,
unlike $p_a$, it has been extensively used as an approximation for $p_a$. This
paper proposes an exact relation between $p_a$ and $p_l$, which cures this
approximation and allows an exact calculation of free energy barriers from
biased simulations.
