Check back weak high cards on monotone boards to realize equity and avoid getting blown off the pot by aggressive check-raises.
Checking is the preferred play here. While we have the range advantage, our specific hand lacks a spade and has very little equity against a calling range.
Note: Betting K-high with no spade on a monotone board is over-aggressive; checking realizes equity better.
Checking back is mandatory. The board pairing the Ace is better for our range than the SB's, but our K-high has almost zero showdown value and no draw.
Easy fold. SB's small lead represents a 'probe' bet, often for thin value or a cheap bluff, but K-high beats nothing but pure air.