Because with replacement, the total number of possible outcomes - the denominator of the probability ratio - remains the same. Without replacement the number of possible outcomes becomes smaller.
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Different lotteries have different schemes and so the probabilities are different.
Conditional probabilities arise when you revise the probabilities previously attached to some events in order to take new information into account. The revised probabilities are 'conditional on the new information you have received'.
I do not add probabilities to anybody!
Empirical probabilities.
Yes, but that might not always make sense.