  [ABRIDGED] The unconditional mass function (UMF) of dark matter haloes has
been determined accurately in the literature, showing excellent agreement with
high resolution numerical simulations. However, this is not the case for the
conditional mass function (CMF). We propose a simple analytical procedure to
derive the CMF by rescaling the UMF to the constrained environment using the
appropriate mean and variance of the density field at the constrained point.
This method introduces two major modifications with respect to the standard
re-scaling procedure. First of all, rather than using in the scaling procedure
the properties of the environment averaged over all the conditioning region, we
implement the re-scaling locally. We show that for high masses this
modification may lead to substantially different results. Secondly, we modify
the (local) standard re-scaling procedure in such a manner as to force
normalisation, in the sense that when one integrates the CMF over all possible
values of the constraint multiplied by their corresponding probability
distribution, the UMF is recovered. In practise, we do this by replacing in the
standard procedure the value delta_c (the linear density contrast for collapse)
by certain adjustable effective parameter delta_eff. In order to test the
method, we compare our prescription with the results obtained from numerical
simulations in voids (Gottlober et al. 2003), finding a very good agreement.
Based on these results, we finally present a very accurate analytical fit to
the (accumulated) conditional mass function obtained with our procedure, which
may be useful for any theoretical treatment of the large scale structure.
