The odds relative to what?
Assuming that non-carbon based life is not intrinsically impossible and furthermore assuming an infinite universe, the odds that non-carbon based life has arisen somewhere in the universe is essentially 1.0. The odds of anything that isn't outright impossible are 1.0 in an infinite universe, including the odds of a world that is identical to ours in every respect except you having the screen name "Jokodo" and me having the screen name "NobleSavage" - if the probability of that happening is only, say 1 in 10^1000000000000 on any individual planet, it just means we'd have to check 10^1000000000000 planets, or roughly 10^999999999977 the volume of the visible universe, to find it. Since we don't know whether the universe is finite or infinite (and how big it is if finite), there's no way could estimate those global odds even if we knew everything there is to know about non-carbon based lifeforms.
So you must mean either of the two following:
1) the odds of non-carbon based life arising on any individual planet, or
2) the odds of non-carbon based life relative to carbon based life, i.e. if we ever make contact with extraterrestrial lifeforms, how likely are they to have a biology that is not based on carbon.
I'd say "very low" for both.
Also, you need to define life.