adverb
1
BAD : It was an absolutely terrible flight. The next time I go to Rio, I will surely go by train.
GOOD : It was an absolutely terrible flight. The next time I go to Rio, I will definitely go by train.
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Surely is used to express a strong belief in the truth or likelihood of what you are saying, and often to encourage the listener to express agreement: 'Surely they should have arrived by now!' 'A twenty-dollar parking fine! Surely someone's made a mistake!' 'You don't need to wear a coat in this weather, surely?'
Definitely expresses a sense of complete certainty about something: 'She said she'd definitely be back by dinner time.' 'This is definitely the best film she's ever made.'
2
BAD : On the first day we'll just stay at the hotel and rest because the journey will be surely tiring.
GOOD : On the first day we'll just stay at the hotel and rest because the journey is bound to be tiring.
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If you feel sure that something is going to happen, you say that it is bound/sure to happen: 'At the interview they're bound to ask you about your last job.' 'Once drivers get impatient, accidents are sure to happen.'
3
BAD : He said he felt worried because of all the recent air disasters. Surely I became worried too.
GOOD : He said he felt worried because of all the recent air disasters. Naturally I became worried too.
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When you mean 'as anyone would expect', use naturally or of course : 'She's just lost her job and so naturally she's feeling a bit depressed.' 'Henry is still in France but he'll be back in time for the wedding of course.'