A choice of one in two, or possibly one in three (6)
I believe the answer is:
either
'a choice' is the definition.
(I have seen 'Choice of two' mean 'either' so perhaps 'choice' could also mean 'either')
'one in two or possibly one in three' is the wordplay.
I cannot really see how this works, but
'one' could be 'the' (both can introduce a definite example of something) and 'the' is present in the answer.
The remaining letters 'eir' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
'of' acts as a link.
Can you help me to learn more?
(Other definitions for either that I've seen before include "Word introducing first of two 16s" , "Each of two; moreover" , "Her tie (anag.)" , "offered a choice" , "One of two alternatives" .)