Phileas Fogg is at the Reform Club, discussing a recent sensational crime with a chap called Ralph. A man has stolen a considerable sum of money—£55,000, no less—from the Bank of England in London. In The Daily Telegraph, a well-known British newspaper, it's reported that the thief was a gentleman rather than a professional robber. It's this assumption that will form the basis of Inspector Fix's suspicion that Fogg himself was the gentleman thief.
During their conversation, someone remarks that the world is such a big place that the thief could be hiding pretty much anywhere. Fogg replies that the world is much smaller due to the remarkable innovations in transport that allow people to move around the globe so much more quickly than ever before. Furthermore, Fogg confidently asserts that the world has become so small, that it's actually possible to get around it in eighty days. It's only a matter of time before someone asks Fogg to put his money where his mouth is, and agree to bet that he will indeed attempt to travel round the world in eighty days.