What made Death Eaters think that they could take on Dumbledore?

Question

In Harry Potter and the Half Blood Prince book, when Draco discovered a secret way into Hogwarts, several Death Eaters agreed to join him on the quest to kill Dumbledore.

Was a way into Hogwarts really an issue? Wasn't Dumbledore himself the real issue? In the previous book, when Dumbledore appeared in the Department of Mysteries, Death Eaters (who were even more expert level than these Death Eaters) started to run away and Dumbledore captured them within a minute.

What made them confident this time? I mean, they weren't going there for other task which they could do secretly. Merlin's beard, they were going there TO KILL DUMBLEDORE.

Answer 1

Snape told them Dumbledore was weakening, and Draco was to be the one to actually kill Dumbledore.

The Death Eaters were likely more confident about invading Hogwarts because Snape was spreading the word to them that Dumbledore was weakening with age. He tells Bellatrix that the fight with Voldemort shook him and he was injured because his reaction time is slower - though the truth was that he touched the Gaunt ring and was cursed.

“Dumbledore has been a great wizard – oh yes, he has’ (for Bellatrix had made a scathing noise) ‘the Dark Lord acknowledges it. I am pleased to say, however, that Dumbledore is growing old. The duel with the Dark Lord last month shook him. He has since sustained a serious injury because his reactions are slower than they once were.”
_{^{- Harry Potter and the Half-Blood Prince, Chapter 2 (Spinner’s End)}}

There were at least five people there fighting for the Death Eaters - Amycus and Alecto Carrow, Thorfinn Rowle (the huge blond one), one who was killed by a stray curse, and the werewolf Fenrir Greyback. With the information from Snape that Dumbledore was weakening, and the knowledge that Draco was the only one who would be held responsible by Voldemort if he failed to kill Dumbledore, they likely did not see it as too risky to invade Hogwarts.

Answer 2

They planned to incapacitate Dumbledore, not fight him.

The Malfoy plan was not based on seeking an open confrontation with Dumbledore. They knew that they would lose in a duel with him.

The centrepiece of their plan was, as user33626 says, the element of surprise. They waited until an evening when Dumbledore was out of the school. Using Draco's contact in Hogsmeade, Madame Rosmerta, they made sure that Dumbledore was going to be away from the school for the night. On his return, they would draw him up to the Astronomy Tower and disarm him before killing him, using the Dark Mark as bait.

"You knew that I had left the school? But of course,” he answered his own question, “Rosmerta saw me leaving, she tipped you off using your ingenious coins, I’m sure.”
“That’s right,” said Malfoy. “But she said you were just going for a drink, you’d be back...”
“Well, I certainly did have a drink...and I came back...after a fashion,” mumbled Dumbledore. “So you decided to spring a trap for me?”
“We decided to put the Dark Mark over the tower and get you to hurry up here, to see who’d been killed,” said Malfoy. “And it worked!”
_{(Half-Blood Prince, Chapter 27, The Lightning-Struck Tower).}

Draco was right; the plan worked very effectively. What the Death Eaters could never have counted on was how weakened and exhausted Dumbledore would be on his return to the school. Voldemort's potion had had a profound effect and had weakened Dumbledore considerably, making the Death Eaters' job easier. Had Dumbledore returned to the school in full strength then its highly doubtful whether Draco would've been able to disarm him. Even in his debilitated state, it took a distraction to actually subdue him, as user931 rightly points out. Dumbledore paralysed Harry with Petrificus Totallus, which made himself vulnerable to attack and gave Draco a split-second advantage. Age also played a part; Dumbledore was a weaker man at his death than he was a year earlier in the Ministry.

“He’s not long for this world anyway, if you ask me!” said the lopsided man, to the accompaniment of his sister’s wheezing giggles. “Look at him - what’s happened to you, then, Dumby?”
“Oh, weaker resistance, slower reflexes, Amycus,” said Dumbledore. “Old age, in short..."
_{(Half-Blood Prince, Chapter 27, The Lightning-Struck Tower).}

Nevertheless, I don't think old age was the primary reason the plan worked. The element of surprise combined with Dumbledore's weakened state was what did the trick. Regardless, the Death Eaters never planned to 'take on' Dumbledore by openly dueling him.

Answer 3

I suppose in this case they knew they had something of the upper hand - they would take Dumbledore by surprise, and it would be several of them against one of him. In the Department of Mysteries, they were chasing after Harry and Co. when suddenly the Order of the Phoenix showed up and alarmed them a bit, and then when Dumbledore showed they panicked because they were already losing. In this case, they were going there under the guidance of someone who knew the layout and Dumbledore had no idea about the Vanishing Cabinets. They were still probably pretty scared, though.