I need to gauge my chances of landing a postdoc - should I send an e-mail to the contact on the job advertisement?
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.