We can manually count the total number of items not in category 2 and divide that by the total number of items. It would help if we added rows and columns for total values:
Category 1Category 2Category 3TotalType A12153Type B344614Type C162520Total628637185
The probability that is is not in category 2 can be found:
Probability of not category 2=1−probability of category 2
=1−18586
=18599
You could also simply calculate the probability of being in category 1 and 3.