As of 16:50 Eastern Standard Time.
As a public service, let’s translate these betting odds into plain English. If a bettor wagers £10 that a majority of voters in Britain will vote to leave the European Union (“leave”), odds of 6/1 implies that the bettor stands to make £70 total: his initial stake of £10, plus a huge profit of £60. (Notice the amounts here are stated in pounds since this is a British betting site, where gambling on political and sporting events is totally legal.) By contrast, if the bettor wagers £10 that a majority of the voters will vote to remain in the E.U. (“remain”), with odds of 1/7, the bettor will only receive £11.43: his initial stake of £10, plus a relatively miniscule profit £1.43. Notice what this particular betting market is telling us: “remain” is a safer bet than “leave.”
prior probability 
It seems to me that there was a lot of hand-wringing but not a lot of analysis as to why the “betting crowd” got the outcome wrong.
Agreed. Almost everyone has overlooked this point, i.e. the fact betting markets also got this wrong.
Not that this is related, but I was also surprised, listening to BBC World Service, that there is apparently some kind of news blackout in the UK on election-day reporting. On-air reporters were carefully crafting their words on the subject that day. I wonder if there is some kind of barrier in the UK to doing exit-polls etc.