I came to ask this question because I couldn't understand an answer in What are the differences between "Marginal Probability Distribution" and "Conditional Probability Distribution"?
In the answer, the chart above is shown, and the difference between marginal probability distribution and conditional probability distribution is explained.
While I understood the difference of the two, I suddenly got a bit confused about the calculation of conditional probabilities.
If P(X = x1) = 0.6, I would expect P(Y = y1) = 0.617.
And if joint probabilities is simply the product of two probabilities, P(X = x1, Y = y1) = P(X = x1)P(Y = y1), then doesn't that mean
P(Y = y1|X = x1) = 0.617, considering the P(X = x1)s will cancel out?
Sorry if this seems like a lazy question. I will definitely try to find out what's happening before an answer.