Who would have imagined that we’d be seeing a fourth season of “Only Murders in the Building,” premiering Tuesday on Hulu? The people who made it, possibly, as they’ve ended each season with a new mystery to be solved in the next. But the very idea of Steve Martin and Martin Short embarking on a television series in their 70s, with Selena Gomez, then not yet 30, as their co-star, seemed as wonderful as it was unlikely — and wonderful is what it turned out to be. Each succeeding season has felt like a little, not-quite-expected gift.

The fading energy of elder statesmen has become something of a hot topic this year, but “Murders” continues to argue for a productive long life. Short, 74 this year, is still in touch with his inner Ed Grimley, and Martin, now 79, is still funny in a specifically Steve Martin way — there were times watching the new season when I expected him to finish a sentence with “and I am a wild and crazy guy” — including some subtle physical humor. Gomez, solemn and low-key — who one could not have foreseen becoming the fulcrum in a May-December comedy trio — provides the perfect balance.

Let us briefly reintroduce our heroes, whom we met as lonely people finding one another around a shared love of true-crime podcasts and the fact that they all live in the Arconia, the grand old upper Manhattan building of the title. They are Charles-Haden Savage (Martin), a largely unemployed actor who starred in a successful late-’80s cop show, “Brazzos,” about which he is happy to remind anyone who stands still long enough to be reminded; Oliver Putnam (Short), a producer of serial stage flops, whose seeming success with the musical “Death Razzle Dazzle” quickly turns sour at the start of this season; and Mabel Mora (Gomez), a smart and artistic but directionless young woman. (She is currently homeless and crashing at Oliver’s; scenes where the trio are all in their bathrobes, discussing the new mystery, are kind of lovely.)

Their relationship, which has had its ups and downs over the previous three seasons, has evolved now to a point of stability, both as friends and collaborators, clearing the deck for action. It’s a new-broom-sweeping-clean sort of season; apart from the welcome return of neighbor Howard (Michael Cyril Creighton), Da’Vine Joy Randolph’s Det. Williams and Meryl Streep as Oliver’s actor-girlfriend Loretta Durkin, there are few faces around from previous years. Personal relationships do not get in the way of the sleuthing.

At the end of Season 3, Sazz Pataki (Jane Lynch), Charles’ former stunt double and longtime friend, was shot through the window of his apartment on the night of the triumphant premiere of Oliver’s play. “Is she dead?” is a question the writers would like you to ask. And also, “Was she the target?,” identically dressed as she was to Charles. These are only the first of many questions this zigzag season will take its time answering.

This season presents a comedy of doubles, stunt and otherwise. Hollywood comes calling to make a movie based on our heroes’ podcast, under the half-mad aegis of executive Bev Melon (a deliciously unhinged Molly Shannon). Even before our trio signs anything, there are a script, a cast and arty twin-sister directors, “hot off their Grand Prix at Cannes and their super-duper viral Walmart ad campaign,” already in place. Where Season 3 played with tropes of the theater, the current series satirizes, or self-satirizes, movies and movie actors. The conceit of characters dealing with people who have been assigned to play them is not new, but it is particularly delightful here, with Zach Galifianakis radiating bored contempt for Oliver, Eva Longoria almost begging Mabel to consider her a peer, and Eugene Levy an excited fan of Charles’ work on “Brazzos.”

The sense of melancholy that bitter-sweetened earlier seasons, with storylines surrounding first victim Ted Kono, grave-robbing deli mogul Teddy Dimas and his deaf son Theo, and Charles’ virtual daughter Lucy, is absent this year in favor of satire and farce and a collection of characters even odder than usual. These include Richard Kind as an Arconia resident with a supposedly ineradicable migrating case of pink eye and Kumail Nanjiani as his neighbor, whose apartment is crowded with Christmas decorations year round. They belong to the building’s less exclusive West Tower, across the courtyard — a different world, where Charles’ Season 1 serial-killer girlfriend Jan (Amy Ryan) lived — upon which Charles, Mabel and Oliver spy like James Stewart in “Rear Window.”

Melissa McCarthy, whose character is apparently a spoiler, will have a lot to do when she arrives, and, as might be said of the season as a whole, she is marvelously funny.

There is a brief trip to Los Angeles, for stock shots, scenes on the Paramount lot and a Hollywood party; a New York bar for stunt performers called the Concussion; and another, longer trip to suburban Long Island. Only seven of 10 episodes having been offered for review; I cannot say whether other locations, or other characters, will come into it. Or what Portugal has to do with any of it.

I can say that I’m sad not to have been sent those final three episodes. We will wait together.