Mystic Duel

In the popular fantasy card game "Mystic Duel", players use two types of magical cards: Sword cards and Shield cards. During a special game mode called "Random Clash", an interesting mechanic occurs.

A player has $s$ Sword cards and $r$ Shield cards placed face-down on the table. Each turn, two random cards are flipped and interact according to the game rules:

• if a Shield card and a Sword card are flipped, the Sword card defeats the Shield (Shield card is removed from play), and the Sword card returns face-down;

• if two Shield cards are flipped, they both return face-down without any effect;

• if two Sword cards are flipped, they clash and both are removed from play.

The pair of cards is chosen uniformly at random among all remaining cards, ensuring two different cards (possibly of the same type) are selected. For example, when two Sword cards and one Shield card remain, with equal probability of $1/3$, the flip involves the $1$st Sword and Shield, or the $2$nd Sword and Shield, or the $1$st and $2$nd Sword cards. In the first two cases, the Shield is removed, and in the third case, both Swords are removed.

Find the probability that following these game rules, at least one Shield card will remain, and all Sword cards will be removed from play.