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Looking at the ladder network: Presumably the resistor values are chosen high enough that as the level rises the fluid shorts out successive resistors in the ladder.
Thus the voltage at the sensor point is: (assuming equal values for R--it is likely they would pick better values to separate the voltage levels better)
12*3*R/4*R (or just 3/4 of 12V) for empty (9V)
12*2/3 for 1/3 full (8V)
12*1/2 for 2/3 full (6V)
and ground for full (0V)
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