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.
A stated value is an amount assigned to a corporation's stock for internal accounting purposes when the stock has no par value. Like par value—which is the face value of a stock stated in the corporate charter—stated value is nominal. The stated value has no relation to market price.