three envelopes with different values you choose one would it be beneficial to trade or keep your envelope

I think this problem is harder than it seems? … I’ve been stuck on it for a while. Typed or handwritten is fine, as long as its clear… I’m trying to understand how to approach this problem in the future and the internet has not been much help.
“I put three marked envelopes on my desk. One contains a check for $1,000,000 and the other two contain a check for $1.00. I let you pick one envelope to hold. I select one of the two remaining envelopes and open it showing you a check for $1.00. Now, I ask you if you would like to keep your envelope to open or instead choose to open the remaining envelope on my desk. (a) What is the probability youâ€ll win if you keep the envelope in your hand, and (b) what is the probability youâ€ll win if you instead choose to open the remaining envelope on my desk? Explain in words, equations, or diagrams.”

Thanks!
 
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