Q:

What is a word meaning "with a low possibility"?

A simplified example:

— Do you think you can come?
— Yeah, unless (word here) I have a visitor.

"not very likely" seems like a solution, but is there any other shorter word/phrase to use?
One of my clients asked me if I was okay to meet with him on the coming Monday morning at 10am.
But I was expecting my mother's visit. She had told me she would visit me either on Monday or Tuesday, but most likely on Tuesday. So, this event was NOT unexpected, but rather what I was not quite sure of its possibility other than it’s low. And so words like “unexpectedly”, “possibly”, “by some miracle” don't fit.
A fuller example:

10am on Monday is fine with me, unless (with a low possibility) my mother visits me, in which case I would have to ask you to reschedule our meeting.

A:

"Improbably" would be acceptable here, if you surround it with commas:

Yeah, unless, improbably, I have a visitor.

Most of the time, though, the sentence is more natural if you put the description of probability at the end, like this:

Yeah, unless I have a visitor — not very likely.

That's basically short for this, the clearest but not the shortest:

Yeah, unless I have a visitor, which is not very likely.

J.R. in comments points out that "happen to have" is a concise way to say this, although it implies a somewhat more likely event:

Yeah, unless I happen to have a visitor.

 

Regarding your more specific example, all four of my suggestions are still applicable with minor adjustments:

10am on Monday is fine with me, unless, improbably, my mother visits me, in which case I would have to ask you to reschedule our meeting.

10am on Monday is fine with me, unless my mother visits me — not very likely — in which case I would have to ask you to reschedule our meeting.

10am on Monday is fine with me, unless my mother visits me, which is not very likely, but in which case I would have to ask you to reschedule our meeting.

10am on Monday is fine with me, unless my mother happens to visit me, in which case I would have to ask you to reschedule our meeting.

A:

In the specific example you pose, the second speaker is indicating that they aren't expecting a visitor to appear and interrupt their plans, but doesn't want to rule out the possibility. If I were in this situation, I'd say:

"Yeah, unless I have an unexpected visitor." 

This both implies that you cannot know if a visitor will come, and also suggests that a visitor is unlikely as visitors are seldom unexpected. The latter suggestion may vary depending on context - for example, unexpected visitors might be more likely at a storefront than at a home.

A:

Update to your update.

10 AM on Monday should be fine, but it's possible my mother will visit, in which case I'll have to reschedule.

I presume if she visits Monday, your Tuesday will be open, so you might be more verbose and just explain the situation. It's possible your client could keep an opening on both Monday and Tuesday until you confirm your mother's schedule.
Original:
In this case I would invert your answer.

Do you think you can come?
Probably, but I might have a visitor.

Here, the first word answers the question, then the conjunction explains why it's not definite. It also seems much more natural to me.
It implies you're expecting a visitor, but there's no reason to specify a visitor unless you're at least somewhat expecting one.
An alternate example where the likelihood is different.

Possibly, but I probably have a visitor.

A more generic answer would be

(Yes,) unless something crazy happens.

Here, crazy means a very unlikely event, like your house catching fire. Substitute with weird, unexpected, or something similar depending on how unusual the circumstances have to be to not go with the speaker.
Also, in normal English, the word yes is understood, and isn't strictly necessary. In the probably and possibly examples above, the interjection is needed because otherwise we wouldn't know how likely it is you'll have a visitor.

