I'm not sure anyone will be able to give you a good quantified "risk" of this.
It's certainly true that there's always risk that you'll be infringing on a bigger player's patent, and if you file a patent and manage to have it go through even though it directly conflicts with a previously existent patent, that's one issue. But that doesn't happen much.
The more realistic issue comes in a small (but very important) distinction of the rights that a patent gives you. A patent does not give you the right to practice your invention. What it does, rather, is gives you the right to stop others from practicing it. It's called a negative right, since you're taking someone else's rights away.
That's easiest to understand through an example. This isn't a brilliant example, as you'll notice, but I think it conveys the theory sufficiently: imagine if I invented a system for collecting questions from people seeking answers and got a patent on it, and you invented a system for collecting answers for people who have read questions, and you got a patent on that. Neither patent is invalid, but it's pretty useless to have an answering mechanism without a questioning one, and vice-versa. In cases like that, we'd usually set up a cross-license that allows each of us to use the other's patent.
Because of that negative right, there's a good chance that a case like the one you're describing wouldn't actually hit the USPTO directly. Most cases of infringement like this would be where the practice of your patent requires use of another one, and the USPTO doesn't really care about that. They care about the contents of the patent, more than their implications (mostly, there are a few exceptions, but generally).
That was a long-winded way of saying that Inventor A's patent is probably irrelevant in this, except on the off-chance that it could be used to mitigate charges through a cross-licensing arrangement if the bigger firm had interest in its invention.
And because of that, this is pretty difficult to really answer. There are a number of factors involved in patent litigation cases--like if Inventor A was knowingly infringing--but of course there is always a risk involved in practicing an invention.
It's also definitely possible that the larger firm, as you've said, will outspend you legally, but that's also true if you, say, slip on a wet floor in their lobby.