I tried, I really tried, to puzzle out what you're saying here, but at this rate, it'll be a lot quicker if someone else just confirms or denies this for me: This is what I came up with, upon reading the Wiki article on Gettier. Is this basically what you're saying?

Situation: I got the job. I believe Jones got the job. I know Jones has 10 coins in his pocket. I have 10 coins in my pocket, but I don't know that. Do I "know" the person who got the job has 10 coins in their pocket?

Classic Gettier Interpretation:

• Belief-Jones got the job
• Belief-Jones has 10 coins in his pocket
• • Conclusion-The guy who got the job has 10 coins in his pocket

Bayesian Gettier Interpretation(Example numbers used for ease of intuition; minimal significant digits used for ease of calculation):

• Belief-Jones probably (90%) got the job
• Belief-Jones probably (90%) has 10 coins in his pocket
• • Conclusion- The person who got the job probably (81%) has 10 coins in his pocket
• Belief-Jones might not have gotten the job (10%)
• Belief-People sometimes have 10 coins in their pocket (50%)
• • Conclusion-Someone other than Jones with 10 coins in their pocket might have gotten the job (5%)
• Belief-The person who got the job probably (81%) has 10 coins in his pocket
• Belief-Someone other than Jones with 10 coins in their pocket might have gotten the job (5%)
• • Conclusion-The person who got the job probably (86%) has 10 coins in his pocket

In case it were unclear, I consider the answer to the initial question "Yes".