Bayesian Network: Independance and Conditional Independance

I'm having some misunderstanding concerning Bayesian network. My main misunderstanding are independence and conditional independence!!

If e.g. I have to calculate P(Burglary|Johncall), is it P(Burglary|Johnca开发者_如何学Clls)=P(Burglary) because i'm seeing that Burglary is independent of Johncalls??

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Burglary is independent from JohnCalls given Alarm. So P(B|A,J) = P(B|A).

Explaining the example

The idea is, that John can only tell you that there is an alarm. But if you already know that there is an alarm, then the phone call from John will tell you nothing new about the possibility of a burglary. Yes, you know that John heard the alarm, but that's not what you're interested in when asking for Burglary.

Conditional Independence

In school, you've probably learned about unconditional independence, given when P(A|B) = P(A)*P(B). Unconditional independence makes things easy to calculate but happens pretty rarely - inside the belief network unconditionally independent nodes would be unconnected.

Conditional independence on the other hand is a bit more complicated but happens more often. It means that the probability of two events becomes independent of each other when another "separating" fact is learned.