How did the agent be so sure that it is a murder?

The answer should be pretty obvious that he took two tickets for him and his wife, but only one on the way home.

That and the fact that you don't "just come" home from a vacation saying "yeah, she's dead." So technically that would be an obvious clue that something happened and he might've know something about her death.

Also I go further and ask myself this: "The man did not inform anyone about the trip." Does that mean that the agent wasn't informed as well? Like he went there by car or by foot? Or just happened to be there and to realize that the husband pushed her off later after he came from his vacation?

Or

There is another version: The couple went to a place that they used it before many times through their agent, but the hotel staff noticed that something was weird and informed the travel agent that the husband left all by his own without even making a reservation through his agency as before. Which it was weird for everyone. So after the husband came home and the sheriff started to investigate, the travel agent made the connections and called the police to inform him of the murder.

These ones are the variants related to the "The man did not inform anyone about the trip." Not even his trip agent.

Just random theories hahaha.