I just flicked through that portion of the book because that’s honestly the first thing I thought of when I read the OP. To me, Ron and Hermione were blindingly obvious once Ginny was properly introduced in book two.
The book describes Snape as almost deranged at the thought of getting revenge on his old tormentors. He was boasting that he would hand Sirius directly to the dementors rather than take him back to the castle. He threatens Harry when Harry insists the prisoners be taken to Dumbledore. Snape gets stunned.
The transformation scene takes place and Sirius shoves Harry out of the way and transforms to fight Lupin. Lupin flees, Harry and Hermione follow Sirius and immediately find him by the lake. The dementors are already attacking Sirius, Hermione goes down, then Harry, staying awake only long enough to see the patronus.
Snape doesn’t wake up until after the dementors have gone. He finds Sirius and the kids out cold by the lake and tells Fudge and Dumbledore that he has no idea why the dementors left before completing their kill.