V, 5 bytes

ç^0/<C-a>

Where <C-a> is 0x01.

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###Explanation

ç                   " On every line
 ^0/                " that begins with a zero do:
    <C-a>           " Increment the number on that line

V, 5 bytes

ç^0/<C-a>

Where <C-a> is 0x01.

Try it online!

Explanation

ç                   " On every line
 ^0/                " that begins with a zero do:
    <C-a>           " Increment the number on that line

V, 5 bytes

ç^0/<C-a>

Where <C-a> is 0x01.

Try it online!

V, 5 bytes

ç^0/<C-a>

Where <C-a> is 0x01.

Try it online!

###Explanation

ç                   " On every line
 ^0/                " that begins with a zero do:
    <C-a>           " Increment the number on that line