  In this Letter we investigate the shape of the probability distribution of
column densities (PDF) in molecular clouds. Through the use of low-noise,
extinction-calibrated \textit{Herschel}/\textit{Planck} emission data for eight
molecular clouds, we demonstrate that, contrary to common belief, the PDFs of
molecular clouds are not described well by log-normal functions, but are
instead power laws with exponents close to two and with breaks between $A_K
\simeq 0.1$ and $0.2\,\mathrm{mag}$, so close to the CO self-shielding limit
and not far from the transition between molecular and atomic gas. Additionally,
we argue that the intrinsic functional form of the PDF cannot be securely
determined below $A_K \simeq 0.1\,\mathrm{mag}$, limiting our ability to
investigate more complex models for the shape of the cloud PDF.
