Well, if the drains aren't plugged on the other 3 (which can happen) then I'd guess that either
A) the hard fuel line at the back of carb bank is seriously gunked up
B) floats/ float needles are stuck or installed incorrectly
C) Drains are plugged, there is gas in the bowls

Fuel is gravity fed from the tank into the bowls and there is nothing to stop it from doing so except the float needles or blocks in the line. Generally I've only had problems with bowls overflowing rather than not filling at all so your predicament is puzzling