What was inside Yuuko's wallet?
( ͡° ʖ̯ ͡°) It's a piece of snakeskin and a receipt from a store in front of a certain station she frequents.
The wallet is Yuuko's because she identified it by the color and unique contents (the snakeskin). The empty face is one of shock and perhaps angst because all her money is gone. The gag here is not the contents but her reaction after looking in her wallet.
In Japan, there is a superstition that goess if you put the cast-off skin of a snake into your wallet, your wallet will be able to accumulate more money. In Japan and other asian countries as well, snakes are a traditional symbol of money and wealth (amongst other things), in Japanese myth some notable ones associated with snake gods are Ugajin and Benzaiten.