  The idea that photons can convert into axion-like particles (ALPs) $\gamma
\to a$ in or around an AGN and reconvert back into photons $a \to \gamma$ in
the Milky Way magnetic field has been put forward in 2008 and has recently
attracted growing interest. Yet, so far nobody has estimated the conversion
probability $\gamma \to a$ as carefully as allowed by present-day knowledge.
Our aim is to fill this gap. We first remark that AGN that can be detected
above 100 GeV are blazars, namely AGN with jets, with one of them pointing
towards us. Moreover, blazars fall into two well defined classes: BL Lac
objects (BL Lacs) and Flat Spectrum Radio Quasars (FSRQs), with drastically
different properties. In this Letter we report a preliminary evaluation of the
$\gamma \to a$ conversion probability inside these two classes of blazars. Our
findings are surprising. Indeed, while in the case of BL Lacs the conversion
probability turns out to be totally unpredictable due to the strong dependence
on the values of the somewhat uncertain position of the emission region along
the jet and strength of the magnetic field therein, for FSRQs we are able to
make a clear-cut prediction. Our results are of paramount importance in view of
the planned very-high-energy photon detectors like the CTA, HAWK, GAMMA-400 and
HISCORE.
