By Nancy Kress.
These are three separate books, instead of one book in three volumes: Probability Moon, Probability Sun, and Probability Space. They have this in their favor: they aren't overly long and the writing is clear and precise most of the time. (The explanation of how the space tunnels work is paradoxical, if not outright self-contradictory.) Probability Moon starts off with a couple interesting premises: one alien race, ancient and apparently extinct, has left the universe space tunnels and other artifacts; a second race has developed that functions on "shared reality", where consensus between its people is automatic and natural, and disagreement causes "head pain" (or headaches). Unfortunately, by the end of the trilogy, it has turned into a morality tale about why humanity isn't mature enough to explore space, and the aliens are basically dismissed.
The author copies a noticeable amount of explanation verbatim between books, which may be a blessing to intermittent readers or those who start with a later book, but I think it would have been better to do something like write "The Story So Far" at the beginning instead of forcing continuing readers to go through, by the third book, multiple pages of copied material. This was probably my pet peeve concerning the book.
What I would have liked to see is an explanation or reappearance of the ancient aliens, and why they created the space tunnels, instead of the same old speculation about how they work based on "macro-level quantum entanglement", whatever that is. I would also have liked to see a reconciliation with the Fallers, the mysterious enemies of humanity, or at least some type of armistice or understanding. Instead, they remain the mysterious enemy throughout, with almost the only human perception of them being that they are extremely xenophobic and can't stand to share the galaxy with other races.
Overall, it has some cute ideas, but doesn't really develop them beyond basic speculation. Probably not worth reading past the first book (somewhat self-contained, although some characters continue into the next book) unless you have nothing better to read (or do).