from the fifth book here are a few reasons why i now believe that sirius is actually dead

Here is what Dumbledore said on
page 825 in OotP the American version:

"It is my fault that Sirius died," said Dumbledore clearly. "Or should I say almost entirely my fault-I will not be so arrogant as to claim responsibility for the whole. Sirius was a brave,clever,and energetic man, and such men are not usually content to sit at home in hiding while they believe others to be in danger."

page 826 in the American version:

'Am I to understand' said Phineas Nigellus slowly from Harry's left, 'that my great-great-grandson - the last of the Blacks - is dead?'
'Yes, Phineas,'said Dumbledore

Dumbledore is considered to be the wisest wizard of all time. Would he make this "false" statement twice if he wasn't 100 percent sure that sirius is dead?