serendipitous

"When we are at a cafe, if I suddenly say it's time to go now, the kids know we immediately leave quietly, because I've spotted someone serendipitously recording us."

With streaming, we don’t really have those serendipitous discoveries any more.

Then, in a serendipitous twist, it gave him a lightning-bulb epiphany about his recently ailing swing.

It takes a lot of time to assemble so many artworks from so many different collections and museums, but the show launched serendipitously not quite a month after Donald Trump was sworn in as president.

That was a reference to the serendipitous conversations that can take place on the margins of a summit or a ceremony as leaders "brush by" one another while they find their seats.