There are two possible situations: 1) when the chosen white counter remains in a bag and 2) when it remains outside the bag.

At the first case the probability of white haven't change. It remains the same as neither the quantity of whites no the total quantity of counters changes. This probability is 1/3 = 12/(12+12+12).

At the second case probability chenges from 1/3 = 12/36 to 11/35 (there remain 11 white counters and 11+12+12=35 total). In decimals it is lowering from about 0.333 to about 0.314.