The princesses are abbreviated r (random), t (truthteller), and l (liar), and you are facing them as they stand in a row in front of you. (their right is our left)

You ask the middle princess, "Does the princess on your right ever tell the truth?"

"yes" answer =

r/t/l
?/r/?

So choosing the princess in the third position will be safe

"no" answer =

l/t/r
t/l/r
?/r/?

So choosing the princess in the first position will be safe