the honest truthful answer is...

"...where it makes the instrument sound the best."

because there is no set spot that is the same on all violins.

It's a trial & error thing and for the most part, it only makes a tiny bit of difference in most relocations.

Usually the post is generally 1 post diameter from the treble (E string side) side of the bridge foot. and directly back from the bridge (towards the tailpiece)

That's a place to start.

to add to Olivers weath of experience, I have noticed some violins actually sound better with the post slightly out of straight up and down. Perhaps it's due to the tuning of the plates or body and back, fit of the post ends or whatever... even if it looks like it's not straight don't worry if it sounds good.

That's the bottom line, does it sound great, then leave well enough alone.

Most schools of thought are that the post should fit just with a touch of tension as it's slid into place. A proper fitted post will have the top and bottom slanted to make as much contact with the front and back as possible, which means they are directional in their construction. Only fit the best in one direction, and the top and bottom are different.

3 mm is only a touch over a 1/10 of an inch. or .118" to be more precise. A typical post needs to be small enough to fit thru the ff hole so usually in the neighborhood of 5.5 to 6 mm in dia is a typical size. That means the post would be 1/2 dia behind the bridge (usually) but some violins like the post further away. Moving the post one way or the other side to side will enhance a certain spectrum of sound, either the E string side or G string side. Some are even tapered at the ends, some are even made from crystals mounted between wood posts (whatever!) but using a wood such as close grained dry, DRY, spruce is the standard. Softer woods tend to collapse and don't work well. The post can't be too long or it exerts excess pressure against the top and bottom unnecessarily and can cause a 'bump' to appear and eventually a "soundpost crack" can develop, (very bad).

I personally have made two posts for mine, and moved them many times seeking that perfect sound, and I feel I have reached the point of diminishing returns... I'm leaving it where it's at for the time being. I can make a different shape and fit of a bridge and affect the sound almost as much. If I were to slack off the tension of the strings all at the same time, and bumped the side with my open palm, the post would dislodge, that's how little interference there is. As the humidity goes up & down you will find a post may get looser and tighter, but as long as there's tension on a string or two everything will stay put except in the worst possible case, you drop it to the floor!

There's a lot already in the forum on the subject, I'm probably just repeating what's already been said. But it is an interesting subject all it's own. I have done quite a bit of test and sound analysis concerning a post and bridge placement and design, and find it almost overwhelming in variables and results achieved.