Do bookmakers have an "underhead" for non-favourites? We all know that bookmakers will add an overhead to their probability percentage in order to protect their profit margins, i.e., an option that has a $70\%$ chance of winning might be given odds that imply a probability of winning of $85\%$.
For non-favourites, would the implied probability be lower than the true probability in order to entice more bets?
 A: Usually the opposite in fact.  It tends to be the case that when gambling people are attracted to the small probability of a large win, rather than a higher probability of a moderate win.  This effect can be neatly modelled by Prospect Theory.
This results in a Favourite-longshot bias that has been studied many times (Google Scholar).  Roughly summarised the implied probability on a long shot is actually most wrong.  Of course it doesn't often look like this because an implied probability of 2% for a real probability of 0.2% only looks like an over-round of 1.8%, but of course in log odds ratio, that is a massive difference.
You will often observe that 100-1 becomes a sort of catch all odds for anything very rare (unlikely teams winning leagues etc.).
Repeated betting on the favourite will lose you money much slower in the long run that betting on the outsider.
A related issue are "accumulators", in these bets people stack together multiple bets one after the other to create outlandish odds from multiple fairly low odds events.  Here the over-round is even worse, and bookmakers can often afford to offer bonuses to attract people to these bets.
To see the issue, imagine betting on 5 events each with a real probability of 20% and implied probability of 25%.  On an single bets your expected return is 80% of your stake (you win £4 when you "should" have won £5).  By the time you stack them together the real probability of winning is $0.2^5 = 0.00032$ but your implied probability is $0.25^5 = 0.0009765$ - in other words you expect to win back only a third of your stake!  This is why a bookmaker can happily offer to "double" your win on an accumulator.
