bare possibility

The bare possibility of it acted as a farther irritation on her spirits; and her being left in solitary grandeur, even supposing the omission to be intended as a compliment, was but poor comfort.

“My guess,” he said, “you can put all of the admissible evidence in half of one book. Most of this is just material. It is not evidence, and it may never surface in the Senate because it is not admissible evidence. Simple theories, of course, are inadequate. That is not evidence. A supposition, however persuasive, is not evidence. A bare possibility that something might have happened is not evidence.”

You must plan experiments on the basis of probability, even bare possibility, rather than certainty.

As Mother Jones’ Kevin Drum explained, “At most, then, we have the bare possibility that out of four years worth of emails, Clinton might – maybe – have failed to notice a proper classification mark on one of them. Why? Because it didn’t include the proper header to warn readers that classified information was somewhere in the body of the email. This is what Republicans want the FBI to spend time investigating.”

In a possible son-in-law respectability, unless quite suspiciously excessive, would not be much "out of place"—not that Don Joaquin admitted more than the bare possibility, till he had fuller certainty as to the stranger's circumstances and antecedents, what he called his "conditions."