Aram is suspiciously NOT random.
I keep getting _Mordekaiser_ both as my first pick and rerolls.
I've also got some champions pretty often (ie. Garen), but NEVER got others (ie. Lux). I mean from my champion collection, of course.
I also remember someone saying that if you first get a melee champion, when you reroll it's pretty frequent (ie, not random) to get another melee champ.
It would be nice to know some stats and data about this mode.
Edit: got Mordekaiser 2 times in a row, again (1 in a reroll, 1 as first draw... Absurd :D)