I have no percentages to give you on this, but observationally and anecdotally I’d say your chances are pretty good — if you have an experienced agent.
Agents don’t take on manuscripts they don’t feel have a market, since they work on a percentage of the deal. The more experienced the agent, the more they have a sense for what publishers want and the more they have the necessary publisher connections for a deal. So your chances are higher.
However, as with any line of work, there are also new and lesser experienced agents. While this lowers your chances of a deal in a general sense, it doesn’t mean they’re not worth considering. Newer can also mean more motivated and willing to put time to an aspiring author’s manuscript. An agent with lesser experience might make up for her lack by being more ambitious and persistent.
Last, you have agents who are dabblers and dilettantes. This is “lifestyle” work for them more than paying the bills. They enjoy the socializing and prestige as much as the income. I’m not disparaging this group across the board, but it’s fair to say they may not be as motivated to land a deal. You see this commonly in another kind of agent — real estate.
So the key, as with all things in life, is to know what you’re getting into. In this case, know the experience and motivations of the agent(s) you approach and (hopefully) get interest from.