What is the relationship between conditional probability and co-occurrence and cross correlation?
I have this example dataset of daily number of occurrences of events A and B:
A alone = 100
B alone = 20
A and B = 5
From this I can calculate the following probabilities
$P(A) = 105/125$
$P(B) = 25/125$
$P(A \cap B) = 5/125$
$P(A | B) = P(A \cap B) / P(B) = 5/25 = 1/5$
$P(B | A) = P(A \cap B) / P(A) = 5/105 = 1/21$
So from what I understand, conditional probability is just co-occurence divided by frequency.
If I have multiple days of this dataset, which probability should I then be comparing over time to calculate the cross correlation between A and B? The co-occurrence $P(A \cap B)$ or the conditional probabilities? And if conditional probability is used to calculate cross correlation, should it be $P(A|B)$ or $P(B|A)$ or both? The cross correlation is asymmetric so I assume the order of the events in the probabilities will be important?
And finally, does this same logic apply on datasets of three or more events?