Ttyjukl

In the book, Harry Potter and the Prisoner of Azkaban, Dumbledore is supportive of Hagrid, that Buckbeak is harmless.

Harry and Hermione go back in time using the time turner and reach the point in the past when the ministry executives come to execute Buckbeak.
While Macnair is about to come out of Hagrid’s cabin within moments to execute buckbeak, Harry is seen tugging Buckbeak’s rope and is still 10 feet away from the forest to avoid being seen. At that moment Dumbledore is found to interrupt Macnair and make him sign a document.
This gives the future Harry time to safe hide Buckbeak.

Footsteps echoed from within the cabin.
“Buckbeak, move!” Harry hissed.
Harry tugged harder on the rope around Buckbeak’s neck. The
hippogriff began to walk, rustling its wings irritably. They were still
ten feet away from the forest, in plain view of Hagrid’s back door.
“One moment, please, Macnair,” came Dumbledore’s voice.
“You need to sign too.” The footsteps stopped. Harry heaved on
the rope. Buckbeak snapped his beak and walked a little faster.

It seems deliberate that Dumbledore, who is against Buckbeak’s execution, is bothering about a ministry document, unless he knew that there would be something in the future,around the cabin, that would lead in the turn of the events.

Does anybody feel the same, that Dumbledore knew of the course of events that would take place?

No canon info, but it's definitely implied that Dumbledore somehow knows what's up. Possibly he spotted them and used Legilimency or...? Just general Dumbledore wisdom.

Note, for example, that he also stops them searching the forest.

"Someone untied him!" the executioner was snarling. "We should search
the grounds, the forest."

"Macnair, if Buckbeak has indeed been stolen, do you really think the
thief will have led him away on foot?" said Dumbledore, still sounding
amused. "Search the skies, if you will.... Hagrid, I could do with a
cup of tea. Or a large brandy."

If Dumbledore could easily use Homenum Revelio without a wand (mentioned by J.K. Rowling), then he could have done so here too and realized there were two Harrys and two Hermiones and that it must have been under his orders that Hermione was messing around with time outside of classes! Here is the quote reproduced:

Angela Morrissey: Why is it that albus dumbledore can see harry under his invisibility cloak at certain moments? (during the series is the cloak only infallible to those who do not own a deathly hallow).

J.K. Rowling: Dumbledore, who could perform magic without needing to say the incantation aloud, was using ˜homenum revelio’ –

J.K. Rowling: ’ the human-presence-revealing spell Hermione makes use of in Deathly Hallows.

So not only does Dumbledore use this spell 'at certain moments', he knows about invisibility cloaks, and had every reason to always be on guard, especially after he saw the diary and knew it was a horcrux that nearly became a living Tom. Remember also that he found/felt a lot of things during the visit to the cave without using a wand.

Can I also point out that in the fourth book when Dumbledoor is discussing a suddenly appearing toilet (the room of requirement) at the Yule ball he randomly winks at Harry, this is never really explained but I'm the fifth book Harry does suspect if Dumbledoor wanted him to know about this room. How could Dumbledoor have known Harry would be to use it. I've toyed with the idea that Dumbledoor uses a time turner but I just can't seem to get it to make sense still there's something else there. J K Rowling told Jude Law a lot of secrets about Dumbledoor (mentioned in a Graham Norton interview) in preparation for fantastic beasts and where to find them. But Jude Law seems to be keeping to his confidentially.