How to compute the conditional probability for a time series given its density estimate?

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Hello to all,
How to compute the conditional probability of a time series having multiple dimensions X belongs to R_d, in a way P(X=xi|X=xj) is the likelihood of observing xj given xi and also the reverse of it P(X=xj|X=xi), provided X fits its density estimate, PX(x)?
Thanks

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