Edit in JSFiddle

//control visibility, give element focus, and select the contents (in order)
ko.bindingHandlers.visibleAndSelect = {
    update:function (element, valueAccessor) {
        ko.bindingHandlers.visible.update(element, valueAccessor);
        if (valueAccessor()) {
            setTimeout(function () {
                $(element).find("input").focus().select();
            }, 0); //new tasks are not in DOM yet
        }
    }
};

var Task = function (name) {
    this.name = ko.observable(name);
}

var ViewModel = function () {
    var self = this;

    self.highPriorityTasks = ko.observableArray([
        new Task("Get dog food"),
        new Task("Mow lawn"),
        new Task("Fix car")
    ]);
    self.highPriorityTasks.id = "high";

    self.normalPriorityTasks = ko.observableArray([
        new Task("Fix fence"),
        new Task("Walk dog"),
        new Task("Read book")
    ]);
    self.normalPriorityTasks.id = "normal";

    self.selectedTask = ko.observable();
    self.clearTask = function(data, event) {
        if (data === self.selectedTask()) {
            self.selectedTask(null);                
        }
        
        if (data.name() === "") {
           self.highPriorityTasks.remove(data);   
           self.normalPriorityTasks.remove(data);
        }
    };

    self.isTaskSelected = function(task) {
       return task === self.selectedTask();  
    };

    self.addTask = function () {
        var task = new Task("new");
        self.selectedTask(task);
        self.normalPriorityTasks.push(task);
    };
    self.trash = ko.observableArray([]);
    self.trash.id = "trash";

    self.myDropCallback = function (arg) {
        if (console) {
            console.log("Moved '" + arg.item.name() + "' from " + arg.sourceParent.id + " (index: " + arg.sourceIndex + ") to " + arg.targetParent.id + " (index " + arg.targetIndex + ")");
        }
    };
};

ko.applyBindings(new ViewModel());

<div id="main">
    <h3>High Priority</h3>

    <div class="high"
         data-bind="sortable: { template: 'taskTmpl', data: highPriorityTasks, afterMove: myDropCallback }"></div>

    <h3>Normal Priority</h3>

    <div data-bind="sortable: { template: 'taskTmpl', data: normalPriorityTasks, afterMove: myDropCallback }"></div>

    <a href="#" data-bind="click: addTask">Add Task</a>
    <hr/>
    <h3>Trash</h3>

    <div class="trash" data-bind="sortable: trash"></div>

    <script id="taskTmpl" type="text/html"><div class="item">
             <span data-bind="visible: !$root.isTaskSelected($data)">
                <a href="#" data-bind="text: name, click: $root.selectedTask"></a>
            </span>
            <span data-bind="visibleAndSelect: $root.isTaskSelected($data)">
                <input data-bind="value: name, event: { blur: $root.clearTask }" />
            </span>  
        </div></script>
</div>

<div id="results">
    <h3>High Priority</h3>
    <ul data-bind="foreach: highPriorityTasks">
        <li data-bind="text: name"></li>
    </ul>
    <h3>Normal Priority</h3>
    <ul data-bind="foreach: normalPriorityTasks">
        <li data-bind="text: name"></li>
    </ul>
</div>

body {
    font-family: arial;
}

h3 {
    font-weight: bold;
    text-align: center;
}

div {
    padding: 5px;
    margin: 5px;
    border: black 1px solid;
}

p, a {
    font-size: .8em;
}

ul {
    padding-bottom: 10px;
}

.ko_container {
    width: 125px;
    min-height: 50px;
    background-color: #AAA;
}

.high {
    background-color: red;
}

.trash {
    background-color: #000;
}

.item {
    background-color: #DDD;
    cursor: move;
    text-align: center;
}

.item input {
    width: 100px;
}

#main {
    float: left;
    width: 150px;
    margin-top: 0px;
}

#results {
    margin-left: 175px;
    width: 150px;
}