How does opponent's flush affect odds of your full house? A cute probability intuition test:
Let $f$ be the probability of being dealt a full house in a five-card poker hand, from a randomly shuffled standard deck.  ($f \approx 0.001468$).
Now look at the case of two players being dealt hands, and player one shows that she has a flush.  Now what is the probability $f_2$ that the five cards dealt to player 2 is a full house?
It seems clear that we will have $f_2 < f$ because if one player has a full house it must be a tiny bit more likely that the other has pairs and other clumps of the same rank, and a flush has none of those.  But to test your intuition, how small is that effect?
Is $f_2$ more than 99% of $f$?  More than 95%?  More than 90%? or less than 90%?
EDIT I had written $h$ for "house" in the first sentence.  Then I used $f$ for "full" later.  
 A: Nice question. I'll give my spontaneous intuitive answer, a quick estimate and then a spoiler-proof exact calculation.
My spontaneous intuitive answer was, like you wrote: "a tiny bit" – something like $99\%$ or $98\%$.
Then I did a quick estimate: The hard part of the full house is the three of a kind. Instead of $13$ ranks of $4$, there are now only $8$ ranks of $4$ and $5$ ranks of $3$, and it's only $\frac14$ as likely to get three of a kind in the ranks of $3$, so the factor should be something like $(8+\frac54)\div13\approx71\%$.
Here's the exact calculation:

There are $5\cdot4\cdot\binom33\cdot\binom32=60$ ways to form both the triple and the pair from a depleted rank.
There are $5\cdot8\cdot\binom33\cdot\binom42=240$ ways to form only the triple from a depleted rank.
There are $5\cdot8\cdot\binom43\cdot\binom32=480$ ways to form only the pair from a depleted rank.
There are $8\cdot7\cdot\binom43\cdot\binom42=1344$ ways to form neither the triple nor the pair from a depleted rank.
Thus the probability is
$$\frac{60+240+480+1344}{\binom{47}5}=\frac{708}{511313}\approx0.001385\;,$$
so the factor is about $94\%$. That raises the question why my quick estimate was so wrong. :-)

