Some best detective and strategy (Chessmaster trope warning! TV Tropes link!) novels have absolutely zero coincidence. They are duels of wits, a game with firm rules and moves chosen as optimal. Contingencies, backup plans, backups of backup plans, foreseeing the next move of the opponent or even manipulating them into making it - a perfectly deterministic setup with zero randomness.
With best detective novels you are getting at first the complete set of clues and rules of the game, and then playing it optimally you can reach the conclusion and authoritatively guess the "murderer" less than halfway into the book. The other half gradually uncovers additional clues, which make the task increasingly easier, until you reach the conclusion - the solution of the puzzle, where our protagonist uncovers the guilty.
In these genres coincidence is a cheap lockpick, a joker card used whenever the author is unable or unwilling to design a fully deterministic reason. It can always be used to explain certain events or finds - but every such use reduces the value of the novel, because instead of rigid rules to be followed in logical reasoning, we have a bit of chaos, something the reader is unable to foresee, and therefore "unfair" in the game which the novel is.
Now, if instead of that, you're writing romance, adventure, horror - you're free to use coincidence. The reader is not expected to foresee the future, neither given enough clues nor able to embrace the nebulous, always-changing rules. It's not a puzzle, it's a ride. Of course you're still able to include "mystery puzzle" elements, be it as short episodes / side threads, or as the central core surrounded by decoration of chaotic fantasy flair. It's an extra flavor, an extra challenge to the reader, and as such, the isolated part should follow the "no coincidence" rules of the game.
But never forget Rule of Cool warning! TV Tropes link!. In short: you don't need much explanation, much exposition or generally going to great lengths with your coincidence if its effects are awesome.
If you compare your painstakingly, precisely built mystery to a house of cards, placing the last card on top of the house of cards is quite satisfying, but crashing a transatlantic cruise ship into it might be more entertaining.