I have a data of 400 subjects from 2 groups, and each group has 200 subjects. Everyone in each group has a unique ID from 1 to 200, and subjects with the same ID are paired (e.g, each subject with ID 1 from group 1 and group 2 are paired). Each one is asked to select an option out of 5 options for a question, and the probabilities of selecting the option are calculated by a mathematical equation. Let's say, as an example, ID 1s from group 1 and group 2 select both option 3 and the probabilities are .3 and .7, respectively.
What I want to do is to compare the probabilities between two subjects in a pair. That is, I want to compare the probabilities of .3 and .7 to see if the probabilities are close enough or quite different. At the beginning, I thought of odds ratio. However, to make a conclusion, I need a distribution of the odds ratio. I know that log odds ratio follows approximately normal distribution, but in this case I don't know how the parameters to create the distribution are calculated because I don't know for sure how the contingency table looks like.
I'm wondering if the distribution of the odds ratio can be constructed or there is a better way to compare them. Any help is very appreciated.