For the purpose of this question, distance means the number of flight hops needed to get from one country to another, with the following conditions:
- Any two points within the two countries count, so you can't pick the least popular airport in the country.
- Only scheduled flights are included.
- No overland transport is allowed, unless transferring within the same city
- Flying over a country doesn't count, you have to set foot there.
- You have to pick the shortest possible route, so you mustn't construct a longer route for the sake of adding more hops.
- Any country on Wikipedia's main list of states works.
- If the direction matters (it's faster to get from A to B than vice-versa), pick the longer direction
My guess would be that it takes three hops at most, but maybe some countries are more remote than that?