  We study the molecular probability of the $X(3872)$ in the $D^0 \bar D^{*0}$
and $D^+ D^{*-}$ channels in several scenarios. One of them assumes that the
state is purely due to a genuine nonmolecular component. However, it gets
unavoidably dressed by the meson components to the point that in the limit of
zero binding of the $D^0 \bar D^{*0}$ component becomes purely molecular. Yet,
the small but finite binding allows for a nonmolecular state when the bare mass
of the genuine state approaches the $D^0 \bar D^{*0}$ threshold, but, in this
case the system develops a small scattering length and a huge effective range
for this channel in flagrant disagreement with present values of these
magnitudes. Next we discuss the possibility to have hybrid states stemming from
the combined effect of a genuine state and a reasonable direct interaction
between the meson components, where we find cases in which the scattering
length and effective range are still compatible with data, but even then the
molecular probability is as big as $95 \%$. Finally, we perform the
calculations when the binding stems purely from the direct interaction between
the meson-meson components. In summary we conclude, that while present data
definitely rule out the possibility of a dominant nonmolecular component, the
precise value of the molecular probability requires a more precise
determination of the scattering length and effective range of the $D^0 \bar
D^{*0}$ channel, as well as the measurement of these magnitudes for the $D^+
D^{*-}$ channel which have not been determined experimentally so far.
