What are other ways of saying "virtually impossible"?
The connotation of pretty much any adverb applied to "impossible" is that there is a known circumstance or set of events that would produce the "impossibility", but that those circumstances are so improbable as to not be worth consideration. "Virtual" itself is defined as "very close to being something without actually being it", and so any term you can think of with a similar definition would be synonymous.
Almost surely impossible - This is from math parlance, in which the phrase "almost surely" has a specific meaning; that the event described has a theoretical probability of one (here, referring to the probability of the "impossible" event not occurring). That doesn't mean the opposite (the "impossible" event) can't happen, just that the chances of it not happening are (N-1)/N for a "large" N (approaching infinity).
Practically impossible - The connotation that it is "impractical" (not worth the cost) to plan for it to happen. Doesn't mean it can't, but the odds are so slim the costs and benefits of expecting it aren't worth it.
Nearly impossible - "Nearly" is a synonym and possible definition of "virtually".
All but impossible, more or less impossible, nigh impossible, near impossible - ditto.
It has a snowball's chance in hell - Slightly colorful and well-known, this one's pretty self-explanatory.
In addition, there are many words or phrases with a similar meaning, "incapable of being considered":
inconceivable, unthinkable, vain, hopeless, infeasible, unachievable, unattainable, out of the question, insurmountable, useless, impassable, inaccessible, unworkable, preposterous, absurd, illogical, incredible, untenable, implausible, unimaginable, unobtainable, not to be thought of, hardly possible, beyond the bounds of possibility, impracticable, improbable, extremely unlikely
KeithS mentioned some possibilities but seems to have blithely skipped over one of the best modifiers, vanishingly, as found in phrases like vanishingly small, vanishingly rare, and vanishingly probable. For examples like the following, see Edwin Ashworth's answer to What word is used to describe an event that will never occur?:
The probability that they coincide by chance is vanishingly small," said coauthor Alan Linde, also of Carnegie.
'The number of complaints which are substantiated is vanishingly small....' (Huddersfield Daily Examiner)
(Ashworth calls the latter an example of misuse, as no fixed finite number can be vanishingly small.)
Infinitesimal captures what you're looking for:
Incalculably, exceedingly, or immeasurably minute; vanishingly small.
Do you ever get the feeling that you are but an infinitesimal speck, swallowed by the vastness of the universe and beyond?
(mathematics) Of or pertaining to values that approach zero as a limit.
You'd use it as an adjective as in "The likelihood of cows flying is infinitesimal" or as an adverb as in "The likelihood of cows flying is infinitesimally small."*
*Actually, I'd say the likelihood of cows flying is non-existent!
A little surprised that no one has mentioned "nigh impossible" yet.
It is an older (even deemed archaic, according to the link) form of saying near or nearly, but still used, though perhaps only in an academic or poetic setting.
"capturing Sardis" - ancient Greek for doing the impossible. Based on the conquering of the ancient city of Sardis in Asia Minor which due to its placement on a cliff was left only one avenue of approach for opposing militaries. This protected Sardis from enemy invasion. That is until Persian forces scaled the cliffs. After entering the city the military unit opened the gates of Sardis for the Persian forces to enter. From that point, the term "capturing Sardis" became synonymous with doing the impossible.