Check to see if the envelope has been opened or torn ‘accidentally’. Send yourself some interesting-looking, but bogus mail. Also be careful not to say anything that could damage your own reputation if it got spread around.
Note: Don’t let them know that you are aware of their spying. If it is, then you have proof that they are listening to everything you say. Then, see if your neighbor repeats this information back to you. Have telephone conversations inside your home and car mentioning some untrue event (for example, you’ve booked a cruise ship vacation, you are thinking of buying a parrot, or you have invited a relative to move in with you something preposterous). If they are the sort of people who seem to delight in letting you know that they are aware of what’s going on in your life, then test them. There’s no point being constantly worried that you are being spied on if it isn’t actually happening.
You have to establish if your suspicions are true. Signs You Might Be Mistaken About Your Nosy Neighbor