Doesn't look like this one is going anywhere, so I will give one of he four cases when observing for two hours.
Case AC -- Both A and C will erupt in the next two hours, but B will not.
Probability of case AC, p(AC), is
Probability that A will erupt, p(A), = 1
x Probability that B will not erupt, p(~B), = 1/2
x Probability that C will erupt, p(C), = 1/3
In Case AC, there is an equal chance that A or C will erupt first.
So Case AC's contribution to the answer is 1/6* 1/2 that A will erupt first and 1/6 * 1/2 that C will erupt first, and 0 that B will erupt first.