Bookies don't necessarily think he might win or lose. They just want people to bet. But I think they do have to make sure they don't create an arbitrage where making both bets creates a no lose situation.In other words, if the bookies are giving better odds (7/2 or $7 to $2) that he won't be confirmed, they believe he will be confirmed.
For example, if the odds were, say, 8 to 1 that Kavanaugh loses (a "no" bet), you could pay $6 for the "yes" bet and $1 for the "no" bet. If "yes" wins, your "yes" wins $1 and your "no" loses $1. That's a scratch. But if "no" wins, your "yes" loses $6 and your "no" wins $8. That would give you a chance to make $2 for no risk.
The real question is whether the collective action of all the betting is an accurate predictor. It wasn't in 2016. Let's hope it's better with Kavanaugh.