Combining Empirical Conditional Probabilities from (One or) Two Samples

Question

From sample $Y$ which contains record of 10m people, I empirically know the following conditional probabilities for different disease conditions:

$P(Death|Condition A) = 5\%$

$P(Death|Condition B) = 2\%$

$P(Death|Condition C) = 2\%$

From Sample $X$ which contains 1m people (might overlap with Sample $Y$, might not, I don't know) I also know the following:

$P(Death|Condition D) = 1\%$

$P(Death|Condition E) = 0.1\%$

$P(Death|Condition F) = 3\%$

Now, how can I calculate the probability of death given two (or more) of those conditions exist:

1. $P(Death|Condition B, Condition C)$ = ? (both from sample $X$)
2. $P(Death|Condition A, Condition E)$ = ? (Across sample $X$ and Sample $Y$, Sample $Y$ is not necessarily a subset of Sample $X$)
3. $P(Death|Condition A, Condition E, Condition C)$ = ? (Generalised version of 1 and 2)

Also, for majority of conditions I have no prior knowledge whether they are independent or dependent.

Any help is much appreciated in advance!

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I did find this thread. But I still have two questions:

1. What are the implications of conditions coming from two different samples with different sample sizes?
2. How do you estimates $P(Death)$ and $P(Condition)$?