Ye've lost yer marbles

The probability is exactly 0.5 that the marble is black.

The situation can be scaled down to the case where there are 3 black and 1 white balls. The probabilities for the are eight possible combinations are listed below. Four end in black:
WB,BBB P=(1/4)=6/24
BW,WB,BB P=(3/4)(1/3)(1/3)=2/24
BW,BW,WB,B P=(3/4)(1/3)(2/3)(1/2)(1/2)=1/24
BBW,WB,B P=(3/4)(2/3)(1/2)(1/2)=3/24

Four end in white:
BW,BW,BW,W P=(3/4)(1/3)(2/3)(1/2)(1/2)=1/24
BW,BBW,W P=(3/4)(1/3)(2/3)(1/2)=2/24
BBW,BW,W P=(3/4)(2/3)(1/2)(1/2)=3/24
BBBW,W P=(3/4)(2/3)(1/2)=6/24

You can see that the probabilities will sum to 0.5 for each ball. Thanks to ZutAlors! for the notation used in the answer.