  We examine how the fraction $f$ of stars for which rotational modulation has
been detected in Kepler light curves depends on the stellar mass $M_\star$ and
age $t_\star$. Our sample consists of $\approx 850$ FGK stars hosting
transiting planet candidates detected from the prime Kepler mission. For these
stars, atmospheric parameters have been derived using high-resolution spectra
from the California-Kepler survey, and rotational modulation has been searched
in Kepler light curves homogeneously. We fit stellar models to the atmospheric
parameters, Gaia parallax, and 2MASS magnitude of these stars and obtain
samples drawn from the posterior probability distributions for their masses and
ages under a given, uninformative prior. We combine them with the result of
rotational modulation search to simultaneously infer the mass-age distribution
of the sample as well as $f(M_\star, t_\star)$, in a manner that fully takes
into account mass and age uncertainties of individual stars. We find that $f$
remains near unity up to $t_\star \sim 3\,\mathrm{Gyr}$ and drops to almost
zero by $t_\star \sim 5\,\mathrm{Gyr}$, although the trend is less clearly
detected for stars with $\lesssim 0.9\,M_\odot$ due to weaker age constraints.
This finding is consistent with a view that the detection of rotational
modulation is limited by photometric precision to younger stars that exhibit
higher-amplitude modulation, and suggests that the detectability of rotational
modulation in Kepler light curves is insensitive to metallicity and activity
cycles for stars younger than the Sun.
