  We determine probabilities of physical association for stars in blended
Kepler Objects of Interest, and find that $14.5\%^{+3.8\%}_{-3.4\%}$ of
companions within $\sim4\arcsec$ are consistent with being physically
unassociated with their primary. This produces a better understanding of
potential false positives in the Kepler catalog and will guide models of planet
formation in binary systems. Physical association is determined through two
methods of calculating multi-band photometric parallax using visible and
near-infrared adaptive optics observation of 84 KOI systems with 104
contaminating companions within $\sim4\arcsec$. We find no evidence that KOI
companions with separation of less than $1\arcsec$ are more likely to be
physically associated than KOI companions generally. We also reinterpret
transit depths for 94 planet candidates, and calculate that $2.6\% \pm 0.4\%$
of transits have $R > 15R_{\earth}$, which is consistent with prior modeling
work.
