In Prisoner of Azkaban, Sirius is caught and locked in Flitwick's office. This is easily accessible by the thirteenth window to the right of the West tower. Someone could just fly up, with any of wizards' many flying capabilities, Alohamora the window and his chains, and fly away. Fudge must know this. So why would they lock him there, instead of a more secure room somewhere else in the safest castle on Earth? Or at least have a guard for the most dangerous criminal ever (or so they thought)?
TL:DR last line.
Fudge indeed knew where Sirius was hiding, or had a clue.
We do know that Dumbledore has quite the authority over Hogwarts which can be defined by the following:
It also seems that Dumbledore has a lot more power due to the last sentence. Enough back story.
At this time, Fudge was still very fond of Dumbledore, and likewise, as he helped him as Minister for Magic in his early days. Due to this, I believe that Fudge would had entrusted Dumbledore with such an important role, as he is the Headmaster of the castle.
With Dumbledore's title, he alone must know the safest place in Hogwarts (which I believe Fudge had thought), and being that it was the Charms professor's office, it would have been exceptionally safe and protected with enchantments.
Seeing as that Dumbledore believed Harry and Hermione's testimony, he would have had full power of the security of the room, allowing them to break Sirius out with ease.
I believe that it comes down to it being Dumbledore's castle, and him having Fudge's trust to place Sirius wherever Dumbledore sees fit.
Because Dumbledore wanted him rescued. I don't have my books on hand, and i will add quotes later.
Dumbledore knew that Sirius was innocent. So he put him in an accessible place, and told Harry and Hermione to rescue him.