I believe that the force that is keeping those water droplets stationery even when the comb is vertical is the cohesion and adhesion of water molecules as they are attracted to each other (molecules near one teeth to molecules near the other teeth of the comb to form a sort of bridge) and also the attractive forces of sticking to the walls of the teeth of the comb.
I should point out that it is not mechanical friction rather it is intermolecular attractive forces between water molecules and with the molecules in the comb that is making a significant contribution because friction depends on the normal reaction force, $R$ by $F=\mu R$ and for a vertical water column here friction is almost non-existent as the water pressure is so low at such small heights so the horizontal normal reaction force would also be very low making friction very low as well.
So you can see that water could easily be held up even without friction. Consider a simple analogy of a hydrophilic surface(attracted to water) being completely vertical(so no normal reaction force and no friction) and a water droplet will stick to the surface and not fall down due to the intermolecular forces with the surface. This can even occur when you have a drop of water stuck to the tip of your finger and held vertically and it doesn't fall(without friction once again as it is vertically placed) due to cohesive and adhesive forces.