As with most UX activities, there should be an overall objective and the process involved should align to meeting the objective.
A/B testing is a common technique used to help guide design decisions, but it should not be the only input considered, so the first thing is to understand what the results mean in the context of the overall design decision to be made.
Often the results provide clues to doing more in-depth research to uncover user needs and requirements, so it can be the first step rather than the last step in making design decisions.
In this case, a general answer to your question would be to:
- Consider how the result fit into your existing knowledge about users
- Decide whether the result is significant enough to warrant further research
- Uncover the underlying user needs and translate them into design decisions
- If it is a trade-off (i.e. A or B), then work out what the alternate use case is and whether it can be designed to cater for both groups.
- Implement the changes and test to validate the assumptions
So you can see that you might not actually end up with having to 'deal with' the minority that chose b, since there can be designs made to cater for both cases or it may turn out that the results are not validated when the changes are implemented.