CSS3 Transition Ease in and out Box Shadow

This could work:

 #how-to-content-wrap-first:hover{
      box-shadow : inset 0 1px 1px rgba(0,0,0,.075);
      -webkit-transition : box-shadow ease-in-out .15s;
      transition : box-shadow ease-in-out .15s;
 }

You need to use transitions on .class and not .class:hover

div {
  height: 200px;
  width: 200px;
  box-shadow: 0;
  transition: box-shadow 1s;
  border: 1px solid #eee;
}

div:hover {
  box-shadow: 0 0 3px #515151;
  ;
}

<div></div>

Here is a resource-efficient solution

#how-to-content-wrap-first::after{
    /* Pre-render the bigger shadow, but hide it */
    box-shadow: 3px 3px 5px -1px #80aaaa;
    opacity: 0;
    transition: opacity 0.3s ease-in-out;         
}

#how-to-content-wrap-first:hover::after {
    /* Transition to showing the bigger shadow on hover */
    opacity: 1;
}