I don't think that this is strictly a question about English; it's a question about rhetoric that could work equally well in any language.
To interpret the man's response, you should think about what was left unsaid.
Woman: The foreign minister is meeting with the opposition on Monday to try to find a peaceful compromise.
Man: None of the meetings so far have had any luck. [Do you] think this one could be different? [I don't think so.]
The fact that he even raised a "What do you think?" kind of question implies that he doesn't think so. If he were optimistic, his response would have been:
Man: None of the meetings so far have had any luck, but I hope this one will be different.
By leaving out the words "I don't think so", he is communicating his pessimism indirectly, and leaving some room for plausible deniability, since the words didn't come straight out of his mouth.