Yes. This is my understanding of their useage, with examples.
I hope it helps!
To determine a problem: When it is believed there may/is a potential problem the problem is identified as existing - but may not be known or identified.
"We now know why your office is so warm. We determined there is a problem with your air conditioner"
To define a problem: - There was an unknown problem - it has now been specifically identified or 'defined'.
"The electrical supply for the air conditioner was disconnected."
To detect a problem: - Only after actively looking for any problems or after investigation (detective work) a problem was found, specific or not.
"We tested the whole building for electrical faults. We detected a problem with your air conditioner although you did not report it."