Lindsay Clancylooks like she has a real shot at freedom after her murder trial ended in a mistrial … and if that happens, she’d probably be thrilled to do what Rachel Danisis doing here … shopping for groceries.

TMZ obtained photos of Patrick Clancy‘s new wife perusing a Whole Foods in Midtown Manhattan on Tuesday … the first time we’ve seen her in public since the shocking end to Lindsay’s trial in Massachusetts.

It looks like Rachel just got done with a workout or a run … and she’s fueling up.

Patrick’s better half wore a gray T-shirt, black workout shorts, and a highlighter-yellow fanny pack … and we’re told she ordered a to-go plate of chicken and string beans at the counter.

Folks who were there say Rachel was very calm while waiting for her food, and she kept to herself … though people around her definitely knew who she was.

As far as we can tell, these are the first photos of Rachel published since Judge William F. Sullivan announced a mistrial in Lindsay’s case Friday … a shocking development, which her lawyer, Kevin Reddington, was none too happy about.

Prosecutors have not yet announced if they’ll pursue criminal charges against Lindsay again … but she could potentially walk free thanks to a legal principle known as “manifest necessity.”

Patrick kept mostly quiet after giving his testimony in court … though he and Rachel were spotted laughing and spending a ton of time together during the proceedings.

However, he’s been more vocal since a mistrial was declared … thanking the jurors and judge — while also noting there will never be closure in the death of his kids, regardless of a jury’s decision.

Patrick — through a lawyer — has also threatened legal action against online conspiracy theorists desperate to pin the death of his kids on him.