The five men who were involved in the bet were skeptical of his success from the start of the book, so their initial doubt helped to encourage their doubt by the end of the story as well. Chapter 36 provides the most evidence as to why the men continue to doubt Fogg's ability to be successful. When the chapter begins, it is the last day that Fogg has to arrive and there is less than an hour for him to do so. Additionally, all reports of Fogg's whereabouts stopped three days earlier. Nobody knows where he is.
The 17th of December, the day of James Strand’s arrest, was the seventy-sixth since Phileas Fogg’s departure, and no news of him had been received. Was he dead? Had he abandoned the effort, or was he continuing his journey along the route agreed upon?
On top of Fogg's seeming disappearance, the last confirmed news that the men had about Fogg said that he was still in jail for a crime that he didn't actually commit. That means a lot of lost time for Fogg. As the chapter progresses the tension builds, and the men's doubt grows. The reason for this is because the clock keeps ticking and Fogg is still absent. With about fifteen minutes to go, one of the men claims victory, because he knows that Fogg wasn't on the train that would have put him in town early enough.
‘Well, gentlemen,’ resumed Andrew Stuart, ‘if Phileas Fogg had come in the 7:23 train, he would have got here by this time. We can, therefore, regard the bet as won.’
Even the reader doubts that Fogg can make it, but with three seconds to spare, Fogg shows up.
At the fifty-seventh second the door of the saloon opened; and the pendulum had not beat the sixtieth second when Phileas Fogg appeared, followed by an excited crowd who had forced their way through the club doors, and in his calm voice, said, ‘Here I am, gentlemen!’