Why is the probability of a didentate ligand to form a chelate with a central atom, high?
Speaking in general, when a molecule is in a "energetic" environment (in this case, for instance, the energy comes from the temperature of the room, about 298 kelvins away from the "zero energy" point), the molecule moves A LOT. It bends, rotates, and changes its conformation.
When EDTA has no complexed metal, its "two arms" just keep moving randomly, until they catch a cation. When one of the arms "catches" a cation, the arms keep moving randomly. But this time, it's much more likely that the other arm will find the cation, being it so close (the cation won't move too far: the other "arm" keeps it close!).
When both arms find the cation, the rigid complex is formed.

To make a stupid example, think about a person with two magnets on his hands, moving randomly in a room in the hope of capturing with both his hands a metal ball: the "first arm" has to search around all the room, but the second one only has to find the first one