Does a probiotic supplement interfere with the efficacy of Penicillin?
Also, are some probiotics destroyed by antibiotics?

Interesting question!

Oooo, I'm dying to give a hint but it would probably give it away!

Probiotics do not in any way interfere with the efficacy of
antibiotics. However, if antibiotics are taken in an interval too
close to your probiotics intake, the antibiotic will kill the
beneficial probiotics you are trying to replenish in your intestines
when depleting these through the use of antibiotics. It is absolute
key to stagger your intake of these respective substances so that the
antibiotics will not cancel out the work you are doing by taking
probiotics.

Here is what I do, as a long-term antibiotics taker (thanks, Lyme
disease): I begin my morning with probiotics with breakfast. When I
know that these have at least gotten to my intestines to some degree,
I go ahead with my first round of antibiotics for the day. Waiting a
few hours is key. When I was taking the two simultaneously, yeast
infections proliferated, unfortunately.

Markvmd's hint probably entails the prefixes of "pro" and "anti" and
"biotics." The pros won't kill, but the antis will!

Spot on, Aliciadenney! I'm surprised you didn't post this as an answer.

Route of administration makes a difference, too-- topical vs oral
(this is a "duh" statement).

Finally, metronidazole and sulfadimethoxine, for example, may be more
likely to work against probiotics than, say, cephalexin.