When I emailed David Hartwell about the idea that this was a single book, cut into three parts for publication, he responded that they were separate and had been published as they came in. He said he thought Kress had had a change of mind partway through and that the end was written while her husband, Charles Sheffield, was dying. I can see that's part of the reason for the lack of connection between books, but isn't that part of what editors are for? (To be fair, Hartwell edited the first and second books only.)
The first book, Probability Moon, was spent on a planet called World and in orbit above it. We learned society, rituals, even some language, and a number of native people. The second book, Probability Sun, had an entirely new cast of characters except for two from the first book. They spent some time on World, most away. This third book had the same characters as the previous one, but spent one short section on World and the plot could have been slightly adjusted to not include that, so I think it was adjusted just to include World since it was the primary focus of the first book.
This book follows on well from the second one, but again, you'd have to read the first book to really get it. We start the book with the tetchy physicist being captured, his older daughter accidentally home, and she runs away. She and her father, plus the primary characters from the second book have harrowing adventures that include growing up, being caught in a revolution, and the end of the world. It's not a bad story. There's just no real flow through the trilogy. I still feel a little cheated. I usually like Kress' books, but I think this series is going to the Friends of the Library.