It’s a really fascinating question and I guess that really the test will be civilisations that are sending out radio waves which will be greater than the spacefaring number.
Nevertheless the size and age of the universe still makes it highly improbable: according to wiki the radius of the observable universe is about 46.7 billion light years and the actual size larger still. Signals from even the moderately far reaches of the universe can NEVER reach us so vast proportions of those potential civilisations can be discounted as just too far away.
Add in the fact that they need to overlap in time: not quite sure my numbers are right but if we assume that a civilisation lasts on average 50,000 years (a rather long time) then there need to be a million civilisations in the life of the universe for three to co-exist at any time on average. Even if there are half a billion that only gives c. 15-17 co-existing at any one time.
Imagine just 15 people evenly distributed on planet earth with semaphore as their only comms mechanism what are the chances they would meet up? (In fact I suspect the analogy is more like 15 snails on the planet with only their eyesight to rely on! And half the snails live in the sea.)
Anyway it is certainly loads of fun to speculate about.