I think that everyone assumed that Sarutobi was going to be the next Hokage, which is why the First and Second told him while they were training him. This is probably the reason that he was being trained by the Hokages in the first place. Plus, he is apparently from an influential family. The Second selecting him to be Hokage at the time was probably only a shock because they weren't expecting him to die, but in naming a successor, he was essentially admitting defeat. Danzo was shocked though, because he was just a jealous old man...even when he was younger.