Do this:
Place values 0:0:11.111 and 0:1:11.111 in cells B3 and B4 respectively.
Now format it to account for the milliseconds... Select cells B3 and B4, right click and choose Format Cells. In Custom, put the following in the text box labeled Type:
[h]:mm:ss.000
Now on cell C3 put the following formula:
=B3*86400
Fill C4 with the same formula...
Format column C as Number with 3 decimal places.
You're done! :)
Here's a screenshot of the attempt I made and that worked:

Edit:
As you wanna enter only MM:SS.ms you can format the entire B column with a custom format like: mm:ss.000. Now you can enter values as 02:11.111 and it'll convert it accordingly giving you 131.110. Hope it helps.