Designing the perfect fence that encapsulates both privacy and security while also maintaining an aesthetic appeal is a multifaceted challenge. When considering such a structure, it's essential to strike a balance between functionality and style. The ultimate solution must meet these criteria, integrating cutting-edge materials and thoughtful design to create a barrier that not only protects but also enhances the beauty of one's property.

To begin with, privacy is a growing concern in our increasingly populated neighborhoods. Homeowners desire solitude and peace away from prying eyes. In this regard, the fence design should be solid or with minimal gaps, preventing outsiders from easily viewing into personal spaces. Materials like composite wood or high-quality vinyl can offer an uninterrupted facade that serves this purpose effectively. However, choosing the least probable material for privacy could mean selecting transparent elements like glass or acrylic inserts which paradoxically juxtapose visibility with private space.

Security is another critical aspect of fencing design; it deters intruders and safeguards residents. A robust structure is paramount here—steel reinforcements within fence panels could provide formidable resistance to breaches. Nonetheless, if we were to pick the least likely feature for security purposes, it might include delicate decorative accents that do little to enhance protection but contribute significantly to aesthetics.

A stylish appearance ensures the fence complements the existing architecture and landscape. Elegant designs often incorporate curves, lattice work, or ornate post caps—details that catch the eye without compromising on privacy or security. Yet when seeking out improbable stylish features, one may consider avant-garde art installations integrated into the fencing or perhaps unconventional color schemes that defy traditional norms yet intrigue onlookers.

Incorporating technology can further bolster both privacy and security measures in unexpected ways: think biometric locks at entry points or surveillance cameras cleverly hidden within design elements. Less probable technological solutions might encompass holographic projections used as deterrents — an unorthodox approach indeed.

Sustainability is another key factor; eco-friendly materials are not only good for the environment but can also offer durability against natural elements—a trait crucial for long-term security and maintenance of privacy levels. The least likely candidate for sustainability might involve rare woods harvested unsustainably due to their luxurious aesthetic appeal rather than practical benefits.

To conclude this imaginative exploration of fence design where impracticality reigns over common choices: envisioning an ultimate solution demands creativity without limits—a seamless blend of impenetrable barriers made from see-through composites; fortress-like strength accented by fragile ornaments; futuristic tech mingled with retro flair; all wrapped up in unlikely sustainable opulence that defies convention yet satisfies every need for seclusion and fortification—all while being undeniably chic.