  We study the OPE coefficients $c_{\Delta, J}$ for heavy-light scalar
four-point functions, which can be obtained holographically from the two-point
function of a light scalar of some non-integer conformal dimension $\Delta_L$
in an AdS black hole. We verify that the OPE coefficient $c_{d,0}=0$ for pure
gravity black holes, consistent with the tracelessness of the holographic
energy-momentum tensor. We then study the OPE coefficients from black holes
involving matter fields. We first consider general charged AdS black holes and
we give some explicit low-lying examples of the OPE coefficients. We also
obtain the recursion formula for the lowest-twist OPE coefficients with at most
two current operators. For integer $\Delta_L$, although the OPE coefficients
are not fully determined, we set up a framework to read off the coefficients
$\gamma_{\Delta,J}$ of the $\log(z\bar{z})$ terms that are associated with the
anomalous dimensions of the exchange operators and obtain a general formula for
$\gamma_{\Delta,J}$. We then consider charged AdS black holes in gauged
supergravity STU models in $D=5$ and $D=7$, and their higher-dimensional
generalizations. The scalar fields in the STU models are conformally massless,
dual to light operators with $\Delta_L=d-2$. We derive the linear perturbation
of such a scalar in the STU charged AdS black holes and obtain the explicit OPE
coefficient $c_{d-2,0}$. Finally, we analyse the asymptotic properties of
scalar hairy AdS black holes and show how $c_{d,0}$ can be nonzero with
exchanging scalar operators in these backgrounds.
