How do these crazy things happen? You know what I mean: Big TV hits arrive seemingly out of nowhere, just when we’ve accepted the assumption that broadcast television is so diminished . . . so splintered . . . so time-shift-viewed, that massive weekly communal viewing experiences are officially bygone.

And then along comes “Little Big Shots,” NBC’s kids talent/variety show.

This past Sunday’s edition, the third, was seen by 13.2 million viewers — by far the high-water mark for a regularly scheduled series this week and (indeed) this season. (Needless to say, the show should again top this week’s Nielsen’s ratings.)

Out of the blue. Or was it?

Let’s go to the reasons why “Little Big Shots” is TV’s champ of the moment.

STEVE HARVEY Never overlook the obvious, and Harvey as host is the obvious. An Original King of Comedy (the touring group of African-American comics, which also included D.L. Hughley, Cedric the Entertainer and Bernie Mac) is terrific here — a master at the slow deadpan, of the fast uptake, of the laugh that appears both spontaneous and genuine. Harvey, as fans know, has been at this kind of television for a very long time. He knows how to read studio audiences and work them, plus his improv skills are top-notch. Harvey’s also been around long enough (30-plus years) to have built a layered fan base, from older to younger. While his stand-up back in the day wasn’t exactly squeaky clean, it was clean enough. He is not Chris Rock, in other words. That makes him not only a familiar presence, but, to a lot of viewers, a comfortable one as well.

FAMILY VIEWING Ellen DeGeneres — one of the executive producers along with Harvey — said in a statement when the show got a second-season pickup last week that “when it’s over, you won’t have to explain what happens in the ‘fantasy suite.’ ” She’s not wrong. This isn’t “The Bachelor,” and that alone leaves the door open, with the doormat reading “Welcome” instead “Beware.”

THE EARLIEST FORM OF TV “Little Big Shots” is the oldest and sturdiest format on television, dating back even to an era when there was no TV, and to showmen like Ted Mack and Art Linkletter, the latter one of the most successful personalities on both media. Linkletter’s “House Party” began on radio just five months before the end of World War II, and lasted until 1969; the CBS daytime version aired from 1952 on. “House Party” was a variety show in the purest sense of the word “variety” — a little bit of this (audience participation quizzes) and that (guest interviews). But the enduring bit over a nearly three-decade stretch was a segment called “Kids Say the Darndest Things,” in which Linkletter debriefed children. Bill Cosby revived the segment as a 1998-2000 series on CBS, but as a cultural and TV fixture — kids saying the darndest things — it has cropped up in dozens of shows before and since. Mack’s “Original Amateur Hour” offered much of the same over its years on various networks, famously showcasing Gladys Knight as a child performer, and Pat Boone.

KIDS DO SAY THE DARNEDEST THINGS The kids here have been cute (that doesn’t hurt) and talented (that either) or just talented at being cute (best of all). Take for example the 4-year-old, Joanna, this past Sunday who proclaimed on YouTube that “I am NOT a princess.” Ahhhhh . . .

And then, while she’s sitting next to Harvey, a tiny princess carriage towed by a Shetland arrives on stage . . . ooooohhh . . .

After that, Harvey points to the father in the audience after Joanna insists he is just “Dad”: “Anyone can be a father,” said Steve. “But it takes a special man to be a dad.” Ooooohhh. Ahhhhhhh . . .

By the way, Jericho will be represented on “Little Big Shots” April 3, when the five children comprising the Joyous String Quintet appear — and do check out the story on them in exploreLI on April 6.

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