In the three-stimulus oddball procedure, there is an infrequent target in a background of frequently occurring standard stimuli and infrequently occurring distracter stimuli. My question is, since the target and the distracter are both infrequent, how do we make the difference between them? Why do we expect different responses to them? Since I am not allowed to answer my question I post here: I assume that the difference is done in the instruction done to the participant.
I assume you are talking about a difference in neural activity?
The difference in processing of targets and distracters does not come from their relative frequency, but from their task-relevance: you are paying attention to the targets, thus increasing gain. In auditory MMN, this attention component becomes evident slightly later than the prediction component, and might be missing completely for ignored stimuli (e.g. when the participants are watching a movie while listening to a stream of sounds). Naatanen has more than one review paper that goes into this, this one probably the most recent.