Why do Lombard, Armstrong, and Blore decide to search the house and the Island?

When they all decide to search the island, they have
decided that the deaths that have already occurred, Anthony Marston and Mrs. Rogers,
"fits too damn well to be a coincidence" (pg 118) They figure out the there is a Unknown
soldier amongst them.  U.N. Owen (unknown), their host. However, they know that the
person is not among them, and they figure that he is out on the island, lying in wait to
kill each of them.  The boat is not coming back for them, and they know that they need
to find him before he takes their lives. Blore meets General Macarthur and says to him
"We're just making a tour of the island so to speak.  Just wondered, you know, if
someone might be hiding on it" (pg 124)