A jar contains 28 marbles. Half of the marbles are red. Half of the non-red marbles are white and the rest are blue. Todd chose a white marble at random and kept it. What is the probability that when Hosea now draws a marble it will also be white? Express your answer as a common fraction.
The jar contains 28 marbles, and since half, or 14 are red, 14 are not red. And of the 14 that are not red, half are white and half are blue, so there are 7 white marbles and 7 blue ones.  If a white marble is removed, there are 27 marbles and only 6 of them are white. So the probability of this marble being white is $\frac{6}{27} = \boxed{\frac{2}{9}}$.