I'm gonna shoot in the dark... but here are my two cents:
Supose that the triangle has an angle . Then you're done.
In other case the other the sum of the other angles so they can't be greather than 90.
¿Then the probability is 1? Not sure
This is a poorly-stated problem and it is not possible to solve it without additional information. The reason is that you must specify some probability distribution in order to "randomly select three positive numbers a,b,c". Do you have more information about the numbers?
(There is no probability distribution which makes all positive numbers "equally likely".)