No, Bob Barker who supplies prison toiletries (hey, someone has to) is not the same Bob Barker from "The Price Is Right."
I love the rumor that he is, and that BB got into the biz because he had a jailed son. When that can be easily disproved because Bob Barker of game show fame had NO children. (Which in itself is very unusual for an 86-year-old man who was married to the same woman for nearly 40 years.)
UPDATE: The Wikipedia entry said Barker had no children earlier. Now it has been changed to say he and his wife had three. Snopes definitely said he had none. Who's right?