Multiply value by row

Hi

I would like to know how can I multiply the value of column three to columns 4-end of file

example of input file:

rs1000012       AK8    2    0.05    0.05    1       0       0
rs10000154      PAQR3   0.01     2       1       2       2       1

Desired output file:

rs1000012       AK8     2    0.1    0.1    2       0       0
rs10000154      PAQR3   0.01     0.02       0.01      0.02       0.02       0.01

Actually I have a file with thousands of rows and 800 columns.
Thanks in advance

Any attempt from your side?

---------- Post updated at 17:20 ---------- Previous update was at 17:19 ----------

Howsoever, try

awk '{for (i=4; i<=NF; i++) $i*=$3}1' file
rs1000012 AK8 2 0.1 0.1 2 0 0
rs10000154 PAQR3 0.01 0.02 0.01 0.02 0.02 0.01