They can project the path 20 years out to be within a disc of a certain diameter with a sigma of some value. They may be 99% sure the asteroid will pass through a disc 48,000 miles diameter, but where within the disc they cannot know. The actual path will be determined by deflection by the gravity of the various planets in the meantime, and the amount of deflection will vary depending how near the asteroid passes in turn to each planet.
The uncertainty increases with each pass near a planet.
Well hell, where the hell is Mr Spock? Don't tell me he couldn't pin this thing down to within 6 inches in about 15 seconds.