I think what you are calculating is the conditional probability of seeing each first, given that you see an eruption in the first hour. But to determine the probability of each being seen first, you need to determine which is seen first if none is seen in the first hour. I calculated those probabilities as 34/45, 7/45, and 4/45. multiply that by the case probability for no eruptions in the first hour, add to the probabilities you have, and you will get the same totals. The probability of seeing A first, given that you have not seen any in the first hour is 76%. And this makes sense if you think of the extreme--if you have been watching for 1 hour and 59 minutes with no eruption, it is certain you will see A in the next minute, but pretty unlikely B or C will erupt in that narrow time window.
Odd probabilities, aren't they?