Why was the (small) Hubble better able to find KBO targets for New Horizons than large adaptive optics ground telescopes? When initial searches for a Kuiper Belt object for New Horizons to fly to after passing Pluto did not find good targets, the Hubble telescope was used, and it resulted in the current targeted flyby for 2019. Initial searches used ground based telescopes. When the search risked running out of time without a good target, the Hubble was brought in to help. 

According to what you read about the current generation of large earth based telescopes that use adaptive optics, those telescopes have a much larger angular resolution and light gathering area than the Hubble. So why was the Hubble better capable of finding a good target?

edit 
Part of the answer may be that the current generation of adaptive optics telescopes only do adaptive optics in infrared, at least if KBOs are best observed in visible light which I don't know but I've moved that to a separate question.

Regarding everyone suggesting that atmospheric absorbtion is to blame, how does that square with this: The 8.3m Subaru telescope (which was one of the telescopes used in the ground search) has a light collecting area of 53m2. The Hubble has a collecting area of 4.5m2. So atmospheric absorbtion would need to be 91.5% for them to collect the same amount of light. Sure atmospheric absorbtion is high for some infrared wavelengths, but surely not that high over all the relevant wavelengths.
I suspect it's a combination of two things:


Stable, guaranteed high-resolution imaging across the entire field of view, something not possible with ground-based adaptive optics;
Very low background in the optical for HST (Hubble), versus a very high background for ground-based AO in the near-infrared.


Most adaptive optics systems are only able to correct in a small region (the "isoplanatic patch") around a bright "guide star" (say, half an arc minute in radius at most); even with artificial laser guide stars, you still need a moderately bright guide star for so-called "tip-tilt" correction. This means you can only do adaptive optics searches in limited parts of the sky.

HST, on the other hand, delivers high-resolution imaging throughout its entire field of view (several arc minutes across), all the time, regardless of where it's pointed.

To make matters worse, the trajectory of New Horizons is close to the Galactic plane, so there are lots of faint background stars. This makes it harder to pick out possible Kuiper Belt objects, making a very accurate and stable point spread function (such as that of HST) even more important.

These searches are best done in the optical, to minimize the sky background. The absence of atmospheric sky glow (mostly scattered light from the Sun and Moon) for HST makes it easier to quickly detect faint sources like KBOs. The fact that adaptive optics systems, as you and Rob Jeffries note, work almost entirely in the near-infrared, where the atmospheric background is much higher, makes it even worse for them.