Yet within three days shall Pharaoh lift up thine head, and restore thee unto thy place: and thou shalt deliver Pharaoh's cup into his hand, after the former manner when thou wast his butler. Genesis 40:13
The Book of Jasher, while not part of the Canon of Scripture, does supply some other interesting details regarding this story. It elaborates on the Biblical account by adding the explanation that "Pharaoh's ministers found many flies in the wine which the butler had brought, and stones of nitre were found in the baker's bread."
Here, we might suppose that Joseph would attempt to improve his own lot through whatever influence might yet remain to these two notable prisoners, and so, it seems, Joseph proceeded to do, as the opportunity eventually presented itself.
Regarding the titles "chief of the butlers" and "chief of the bakers", we find in the New Bible Commentary, Second Edition, the thought that these two were probably high-ranking officials of the Egyptian court. The New Bible Dictionary, under the item "Cupbearer", states:
"The 'butler' of Joseph's pharaoh...both in Hebrew and by function was the king's cupbearer." Further on, the same note states: "The Egyptian cupbearers...were often called 'pure of hands', and in the 13th century BC one such cupbearer is actually entitled...'cupbearer (or butler) who tastes the wine'... These officials (often foreigners) became in many cases confidants and favourites of the king and wielded political influence... ."
So we see that the positions were, indeed, ones of great trust, and of high personal responsibility for the Pharaoh's well-being.