No, the Preferred shares don't convert at $3. That's the value given to them as Preferred Shares. When they convert to common stock they are at the value of the common. You can apply any value to a Preferred share.
There's no magic that bumps the share price to $3 or $1 as the other issuance has the stated value at.
There's also no conversion requirements for price put on those Preferred shares.