AWK, 120 118 bytes

{while(i++<NF)r[i]=int(rand()*NF)+1;for(;l++<NF;j=k=0){while(k++<NF)if(r[k]==l){printf"%*c",k-j,$k;j=k}print FS}}

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I've included the 5 bytes in the score for the necessary -F '' switch, but I had to use the BEGIN{FS=""} directive for the TIO link since it doesn't process the command-line switch properly.