If other people can fall off a boat and wind up on Zaroff's island, why not Rainsford?
Though there may be some need to practice "suspended disbelief" with this story, if we accept the premise that the island exists we should accept the fact that Rainsford lands on the island too.
Disbelieving one aspect of the story, we have to apply disbelief to all of it and vice versa.
You could easily argue it is not his fate but his arrogance that made him fall off the boat at that particular spot. While Whitney and the crew heeded the warnings and legends of Ship Trap Island and thus retired to the cabin early, Rainsford remained defiant and in a way challenged the myths of the island by staying out alone on the deck at night smoking a cigar. There is no coincidence that Rainsford went overboard, while the rest sailed safely through. Rainsford's arrogance more than fate led to his stay on Ship Trap Island and his meeting with Zaroff.
Wow. How sad that with this marvelously crafted story the question that arises is what are the odds that Rainsford would end up there. It doesn't even take much suspension of disbelief to accept this as Connell has crafted several details to make this possible.
In both movies and literature, there must be a "willing suspension of disbelief" on the part of readers and viewers. We do it all the time. Think about movies like Star Wars, Lord of the Rings, Harry Potter, and Avatar--they all have, at the core, a premise which is not real, or even possible. Yet we watch and we're transported to other times and other places, watching things that couldn't really happen. It's not real, but we buy in and enjoy the ride.
In literature, the same is true. In Lord of the Flies, for example, we don't really have a sensible explanation of how the boys got on the island; yet we read with interest and get the point. The same is true here. The odds are high, but it happened and we go from there.
To best answer this question, one must first interpret and analyze the events leading up to Rainsford's fall overboard. Rainsford, the story tells us, is a pipe smoker, and one of his cherished possessions is his briar pipe. It stands to reason that one would pursue an object of value or worth if it was imperiled, and that is exactly what Rainsford does, even though his efforts were somewhat "overdone." As a result, he ends up plummetting into the sea like the pipe which was bumped from his mouth, and he is washed ashore on Zaroff's island. Stranger things have happened, and in this story the probability that one would wash with the tide into a land mass may be slim, but perhaps that dim chance of a bright hope is what makes the story endearing in the first place.
One of the things you learn as you read more and more is that many works are based on accidents and coincidence. Most reader accept that and learn to suspend their belief to enjoy the story. However, if you cannot accept the author's attempt to get you to suspend your belief, then that particular author has not achieved his effect with you. Many people simply accept the opening of the story as possible but improbable and go on without much thought. I agree that the odds of Rainsford falling off the boat and just happening to end of on the general's island are not likely.However, I was able to suspend my belief and enjoy the rest of the story. For you, this event was not possible and so you may have been tempted to reject the rest of the story. That's why we study literature, to appreciate or reject how each author attempts to show us something about life.