Why did Han Solo end up with Jabba the Hutt?

The Empire hires Bounty Hunters to track Luke (and the Rebel band), of which Han is an accessory to: if not a rebel himself.

The Rebel band (Han, Chewie, Droids and Leia) seek refuge at Bespin, as its supposed neutrality is supposed to offer them some form of protection (or at least not immediately reporting their presence to the Empire), not to mention Han's relationship with Lando.

This plan would have worked, if Boba Fett had not tracked the Millennium Falcon to Bespin, by hiding Slave 1 amongst the debris/refuge field discharged by the Super Star-Destroyer.

By plotting their trajectory (and applying some deduction) Boba would have been able to both trail the Falcon and report their destination to the Imperial Fleet.

As Solo was meaningless to the Empire (except to demoralize them by witnessing him being frozen in Carbonite, and to test whether a Human would survive the process so as to transport an unwilling Skywalker), part of his fee was implied to be Solo: Vader's foreknowledge of Jabba in the "he's no good to me dead" conversation infers a previous agreement/discussion between Fett and Vader.

So Boba was able to claim one bounty whilst picking up the necessary cargo to claim another: it's obvious negotiation.

However, there is another glaring plot-hole hidden within this sequence that goes un-addressed: maybe someone else would like to ask it (it might already have been asked!), but...

How did the Empire beat the Falcon to Bespin, if the Falcon is the 'Fastest Ship in the Galaxy' and Vader "arrived just before you did (...I'm Sorry)"?

In fact Boba Fett (as well as the other bounty hunters after Han) worked for Jabba, who had put the bounty on Han because he owed him money, as we learn at the beginning of Episode IV and which he (Han) states himself when leaving Hoth:

Well, there's a price on my head. If I don't pay off Jabba the Hut, I'm a dead man.

Boba Fett has never explicitly worked for the empire or had any other motivation than the bounty he was tasked with, so the only place Han could end up after given over to Boba was Jabba's lair.

Darth Vader hadn't any interest in Han Solo at all, which is why he tests the carbonite machine on him, he didn't care if he died, ended up with Jabba or whatever, as long as he was out of the way (and Tatooine would likely not hold a nice future for him). Everything Vader concetrated his efforts on was the young Skywalker and the others had played their roles in setting up the trap for him, what happens to them now is out of his narrowed down view.

As we know from this meme, it was due to a debt to Jabba. Bobba Fett was just there to collect the bounty. This was made evident in the re-working Lucas did on A New Hope, where a scene with Jabba the Hutt was added to enforce the fact that Han owed him money. For those of us old enough to remember a time when Han shot first, you know Jabba wasn't in the original theatrical release.