  We provide hadronic input for the $B$-meson semileptonic transitions to a
light pseudoscalar meson at large recoil. The $B_s\to K$ form factor calculated
from QCD light-cone sum rule is updated, to be used for a $|V_{ub}|$
determination from the $B_s\to K \ell \nu$ width. Furthermore, we calculate the
hadronic input for the binned observables of $B \to \pi \ell^+ \ell^-$ and $B
\to K \ell^+ \ell^-$. In addition to the form factors, the nonlocal hadronic
matrix elements are obtained, combining QCD factorization and light-cone sum
rules with hadronic dispersion relations. We emphasize that, due to nonlocal
effects, the ratio of branching fractions of these decays is not sufficient for
an accurate extraction of the $|V_{td}/V_{ts}|$ ratio. Instead, we suggest to
determine the Wolfenstein parameters $A,\rho,\eta$ of the CKM matrix, combining
the branching fractions of $B \to K \ell^+ \ell^-$ and $B \to \pi \ell^+
\ell^-$ with the direct $CP$-asymmetry in the latter decay. We also obtain the
hadronic matrix elements for a yet unexplored channel $B_s \to K \ell^+
\ell^-$.
