I need to gauge my chances of landing a postdoc - should I send an e-mail to the contact on the job advertisement? I'm a recent PhD graduate looking to work in academia. I have applied for an assistant position (let's call it position A) that I think I have good chances of getting, that starts really soon. However, there is a postdoc position advertised (let's call it position B) in a different institution, which I think would be more beneficial to my career, and which starts a few months later. Trouble is, if I apply for position B now I won't hear back from them until after position A has already started. Also, position B seems to be far less certain.

So I need to gauge the relative risk involved in refusing position A if I get an offer. I was thinking of emailing the contact for position B beforehand, saying something like "I have such-and-such qualifications, do I stand a chance?" but then again I don't want to put them on the spot or make a bad impression. I mean, I know that they can't guarantee I'll get position B, and I don't expect that, but there's the danger that they may interpret my e-mail in this way. I'd like to explain to them that there is another position that I have very good chances of getting, so I need to calculate the risk (again, I know that I may end up not getting position B anyway, I just want to know if getting it is a serious possibility). Should I send such an e-mail, and if so, how should I word it so that it is received well?

I should also mention that I have personally met the contact in question and discussed my work with them in the past, and they will remember me in that respect. At the very least, I'd like to not ruin this relationship.

I really don't know what the right thing is, and I hope you'll understand my anxiety. Any advice will be appreciated... thanks!
You seem to answer the question yourself that there would be no problem of interpretation. It is just an inquiry. However, you are not likely to learn very much absent a formal application giving the new institution to compare your credentials with those of others. But I see no particular reason not to ask. 

However, there are other avenues you might want to consider, depending on how flexible institution "A" is. You haven't been offered anything there, nor certainly accepted it, so you are free to apply to the other place. If you then hear encouraging words you can try to explore at least a delay with "A", informing them that you are undecided about another offer or opportunity. There is risk in that, of course, but if you don't apply for the second position you don't have any chance at all.