The issue here is that even if partner had played the ♠Q, on the first trick, rather than the ♠K, there are limits for you to be able to know what is going on. You must determine what you think is going on and go with that.
There are, to be sure, clues, and one of them gives a pretty definite answer about what to do. But it does not rule out other possibilities requiring a different play. Before I go into that helpful information, here is a little context: when East plays the trump king, it may not be a singleton nor lowest of touching honors. When partner makes an opening lead against a suit contract in a side suit, we need to tell her, most of the time—this is bridge, remember, there are always exceptions—as much about our holding in that suit as we can with the card we play so she can know what to do on defense.
But when partner leads a trump, things change. Third seat can play whatever card she thinks will make life harder for declarer. Third seat is not—again, most of the time—completely concerned about revealing her trump holding to partner. Partner may false card in attempt to fool Declarer.
Turning to the wealth of information for ducking, when partner plays the ♠K and Declarer wins and leads the ♠10, it is highly likely that Declarer does not hold the ♠Q. The reason is best seen if we look at what he would do when he does hold the ♠Q. When East plays the ♠K on the opening lead, it may be from a few holdings, including ♠KJ and ♠Kx. The reason to play the K is, if Declarer holds ♠AQ10xx(x), playing the ♠K sets up partner’s ♠J. So, if Declarer had held ♠AQ10xx(x), and had East ducked the spade, the defense would have gotten no spade tricks.
Moreover, if East did hold ♠K and J, Declarer may fear that East actually holds ♠KJx. Having ♠AQ10xx(x) himself, he might have returned to dummy in a side suit to take a finesse in spades, protecting against such a holding.
Secondly, Declarer, again assuming a holding of ♠AQ10xx(x), may decide not to worry about the ♠J and just plop down the ♠Q. One rationale for such a move, besides lazy thinking, is that if the ♠J does not fall, it would be to Declarer’s advantage to leave it out, so that he can eventually throw in whoever holds the ♠J later for an end play.
So, if Declare holds the ♠Q, it is highly likely that he would go to Dummy to take a finesse against East or play it next.
Declarer did none of those things. That strongly suggests he does not have the ♠Q.
There is a second scenario, though, however rare. That is that Declarer has a 6-card spade suit, reads East’s play of the ♠K as a singleton, thereby placing West with two outstanding spades, the ♠Jx, and a sure spade trick. Deception in bridge is based on knowing how an opponent will, in this case, defend a deal and then to play in such a way as to fool him into playing it wrong. If the great Zia Mahmood, considered to possibly be the most devious bridge expert of all time, was declaring and decided that the only chance for an extra trick was to trick you out of your ♠J, then he would lead the ♠10, hoping you will duck for the very reason that you will conclude your partner holds the ♠Q. If you hit upon this scenario, as you think about whether to play your ♠J, consider whether Declarer is good enough to make this kind of deceptive play.
There is no sure-fire way of getting your play to the second round of spades right. You must think it through and then go with what you decide is the best play. The odds strongly favor ducking the ♠10. But Declarer may be channeling Zia and you will kick yourself when the ♠10 holds and he next plays the ♠Q.
Two other points are worth making. First, if your partner finds herself in the same situation as described above, and after thinking about it, gets it wrong, show sympathy for her. That’s what being a good partner is about. It could just as well have been you. Be the only friend in the room she has when things do not go her way through no fault of her own (and even when she is at fault).
The other point to note is that, in assessing a defensive situation, decide how Declarer would normally play the deal holding the card you are concerned about, i.e., if he held that card, he would play one way; if he doesn’t hold it, he will play another way. That type of analysis is good defensive thinking at the table. What that means is that the better you become as declarer, the more you know the way declarer is likely to play a hand. You can apply that knowledge when you are on defense.
Doing that will make you a very dangerous opponent indeed.
| 
